What is democracy?
There's no real consensus on what democracy actually is. Rather than there being a clear definition that separates a democracy from a non-democracy, scholars just generally agree that they are roughly all talking about the same thing, though there's plenty of room for disagreement and diversity. There are all sorts of ingredients that people propose for democracy (votes, representatives, institutions) and there are all manner of types of democracy (direct democracy, deliberative democracy, associative democracy, participatory democracy, representative democracy), but no "one, true democracy". But the concept of democracy means something, and even though an exhaustive survey isn't something there is room for here, there are a couple of key points that I think are worth pointing out.
So here's my shortlist of concepts that make something democratic. A different democratic theorist might disagree - they might want to add something, or remove something, or place something into a different context - but I think this is a justifiable starting point.
People
Maybe the most defining feature of a democracy is the principle that the people are the ones who hold the power. Democracy answers the question, "Who rules society?" with "the people". This contrasts with other styles of rule, where the answers might be "the monarch" or "the rich" or "one special family".
The next questions are then, "Who are the people?" and "What does it mean to have the power?" Here the answers vary greatly. Today, the answer to the first question might be "citizens over 18 who aren't serving long sentences in prison", which is somewhat inclusive but still has distinct exclusions. Earlier in history women were typically excluded, and people who didn't own land, and often people who weren't the right ethnicity. So the idea of "the people" can be a little flexible though, over time, more and more people have tended to join "the people".
As to what it means to hold the power, this varies as well. A common answer for modern democracies is that the people have the power to consent, or confer, power to representatives. The typical modern democracy is a representative democracy, where the people don't exactly rule, but they choose which representatives will rule (and on the basis, supposedly, of what rules they will make). Another answer is that the people choose the policies and the laws themselves - a process known as direct democracy. These types of power are procedural, because they are enacted by following agreed upon procedures, such as elections and referenda.
Another type of power is the power to say things, to move about, and to form groups. These are all essential ingredients for getting a lot of people to agree with you and carry out ap lan of action, such as an election campaign, an awareness campaign, a protest, or something similar. The power to say things means that people can say when they think the government is wrong, or point out what the government is doing.
The most controversial - and perhaps fundamental - power is the power to use violence. Normally violence is a bad thing, of course, but often democratic theory suggests that there are two very good reasons to use violence. The first is when the people, either directly or through their representatives, have made a law, and the law needs to be carried out. So, for example, putting a murderer in prison involves violence. The second is when the people withdraw their consent from the government but the government keeps ruling anyway. At this point a lot of theorists will suggest that it is okay for the people to use violence to remove the government and restore order.
Some theorists decribe some clear criteria to look for in order to check if the people have the power. One of these is checking that enough people are included in "the people". There are at least three ways to check: can people of all sorts vote, are people of all sorts representated in policy-making, and are people of all sorts represented in the outcomes of policy? If, for example, a minority group can't vote, then the suggestion is that government isn't really consented to by "the people". If they can vote, but they aren't really represented in a democratic assembly (that is, their candidates don't win seats), then government isn't really representing "the people". If they have successful candidates, but the laws that successful candidates make don't really respond to their interests and issues, then government isn't really working for "the people".
Another significant criterion is whether the people have enough of different sorts of power. Having voting power is one thing, as is having the power to speak, but there are other sorts of power like knowledge (and access to education) and money (and the ability to run campaigns and make change). There's also representative power - having people a lot like you in positions of power already, to try and ensure there isn't regular bias.
One of the fundamental concepts associated with the people having the power is that of equality. The concept of equality says that people should have the same amount of power, and be treated the same way - that each person gets the same power in their vote, and is treated the same way by the law. Equality is another one of these concepts where there are a variety of interpretations (equality of which powers? and of which treatments?). There are times when advocates of democracy specifically suggest that equality is not the best idea, such as when accounting for some disadvantage.
So for some giving people the vote is enough for a system to be a democracy, while for others there also needs to be other things in place: limits on government power, inclusive policies, low wealth inequality, and good access to education.
Collective self-determination
The next question that democracy tries to answer is, "What do the people do with the power?" Here, I think, there are three main answers. The first is collective self-determination.
If an absolute monarch were to rule over the people, then the monarch could make any decisions they want about the people and their society. If the people rule themselves, what does it actually mean for "the people" to make decisions? Well, it could mean that each individual person makes decisions for themselves. Or, it could mean that the people make decisions for everyone as a group. This latter one is the idea of collective self-determination. The people see themselves as a group, they know their future is bound together as a group (perhaps whether they like it or not), and they need to make decisions "by the people, for the people", as Lincoln put it.
So collective self-determination is about the people choosing what laws and policies should affect the whole of society. The question is not, "Do I think murder is bad?" but "Is murder bad for society?" (and what should we do about it?). Another way to think of it is to ask, "What sort of society do I want to live in?"
There are really two main things that collective self-determination focuses on. The first is rules that apply to everyone, such as everyone driving on the left (and not everyone choosing for themeselves). The second is the ability to organise projects that can benefit everyone, such as healthcare and public transport.
What's really at the heart of collective self-determination is not that there are objective or clear answers to these questions, but that the answers are the right answers because everyone decided them together. For many democratic theorists, there is no better way to answer questions.
The common good
But for others, there is a second answer to, "What do the people do with the power?" And that is that people pursue and discover things for the common good.
In some ways, this is pretty similar to the previous answer. The difference is that for collective self-determination the answer is the right answer because it was answered by the people, whereas for the common good the answer is the right answer because there is an objective right answer - it's just that the only way to find that right answer is to have people come together.
So collective self-determination could come up with a policy of burning fossil fuels and polluting the air, and it would be the right decision because "the people said so", whereas for the common good it would be the wrong decision because "it's not good for the people". Critics of the former say that it is not a sufficiently good way to think about democracy because people can make stupid decisions, whereas critics of the latter say that there is no other way to determine whether something is good for the people or not other than the people deciding it collectively.
Peace
The third answer to "What do the people do with the power?" is "Be peaceful." Democracy is pretty good at keeping things peaceful. If you don't like the government, there is a way to change governments without having to use violence. If you don't like a law, there is a way to change laws without using violence. If you don't like a law, you'll likely agree to follow it anyway, because at least the process of making it was fair and it's not worth breaking it when you can possibly change it later. The laws also keep things predictable, and the fact that the power lies with the people means that governments don't want to cross them too much.
Of course, no democracies are without violence - it's just a matter of how much and who it is directed at. But perhaps democracies are generally safer than other types of rule, and more stable than places where who is going to rule is in contention.
Individual autonomy
Part of the promise of the people having the power is that the people, individually, can go about making decisions regarding their own lives. Now, different forms of democracy disagree on how much individual autonomy people should have - can they say anything and go anywhere? But a major part of the theory of democracy is freeing people from the oppression of a monarch or a tyrant. So while some forms of democracy focus on people making decisions about what sort of society they live in - and, as such, how much individual autonomy they want to provide themselves with - other forms of democracy declare a minimum amount of autonomy that can't be taken away.
The core concept here is that people should be, as much as possible, able to live the lives they want to live, and able to pursue their own happiness, and able to define and follow their own path of flourishing. A system that somehow has collective decision-making but doesn't have any space for individual autonomy or flourishing is likely not to be called a democracy at all.
Proceduralism
The last main concept I want to raise is proceduralism. There are many ways that the people can make a decision together, and there are many complexities to consider as well. This means that there are lots of ways that people can find sneaky ways to be unfair. Perhaps they use different decision-making procedures depending on what outcome they want, or who they want to include in the process. Perhaps there are a lot of steps involved, and one or two of them can be passed over without others noticing. If there isn't much information on the process, maybe some people are at a disadvantage because they are unfamiliar with it and don't know when it is being used unfairly.
One answer to this is proceduralism: we pick a procedure, make it known, make it comprehensively include everyone and everything we think is fair, agree on it together, and stick with it. There are lots of different methods for electing candidates to a democratic assembly, but the same one is used over and over again unless we use an agreed upon procedure to change it. Democracy - large-scale, state-run institutions of democracy - all have established, debated and often highly technical procedures.
So these are my picks for the main concepts of democracy to example: the people having the power, coming together to use the power for their own benefit (such as collective self-determination or the common good), the goal of a peaceful society, and the use of procedure to make it work smoothly.