I think you asked the right question.

Free will historically has been defined as either a sort of free action, that we can act upon our desires without someone else stopping us, or a free choice between two actions. If you are ever in question of whether something is down to free will or not then consider the act of a person morally. Do you think they're responsible for their action, if not, why not?

If I agree to meet you at the bus stop and oversleep, you might feel that I've wronged you because I am responsible for me getting up on time and being there. If I told you that I wasn't there on time because I was mugged on the way to meet you, you (hopefully!) wouldn't think I'd wronged you because it was outside of my control. This encompasses the first definition, that it is my action independent of others.

What about if I agree to meet you at the door of my house and I wake up on time, but because of my severe OCD I am late to meeting you. You may feel wronged that I took so long, but upon realisation that I have to check all the light switches are off before I can come to meet you, you may feel that this was outside of my realm of control. In this example I didn't have any other choice to checking all my light switches, it feels intuitively that if someone is to be held morally responsible they ought to have had an option to refrain from the action.

So you might hold that free will is the ability to do as we want and the ability to have a choice in what we do. That's a standard compatibilist view. Compatibilists believed that we might be in a deterministic universe; one where the facts of the past and the laws of physics entail what will happen in the future. It's easier to imagine it like a billiards' table where if one ball is hit with that knowledge and the knowledge of physics you can predict where everything will go. The compatibilists said that if we were in a deterministic universe, although current scientific findings predict that we aren't, we might still have free will in the sense already given.

Okay, I should back up to why Science says we aren't. Billiards and conventional rules work absolutely fine for Newtonian physics, but the second you even edge in quantum physics all our rules hit the wall. I'm a hundred percent sure I could be rightfully called out on this one, but quantum effectively shows us that there are some things we can't predict through laws of physics, we just have to measure them and see what they are. We don't know how nuclear particles decay, Heisenberg's Uncertainty Principle kinda screws us over in humans ever knowing what these minute details of the universe are; the closer we measure the velocity of an atom the less we can know about the location of it and vice-versa. If there were a Laplacian demon in existence that could know all these things, it couldn't exist in our universe as any physical entity for fear of adjusting something about the universe and having a recurring issue of predicting. Heisenberg's UP doesn't show it can't be deterministic, but it does show that we could never be the determiners and it does show it's really unlikely that the universe is deterministic.

The compatibilist stance is just one of the many stances on the issue. If you're really interested in a light book on the topic, Dennett writes quite well on modern Compatibilism (I personally really enjoyed Elbow Room) and argues our free will is controlling our future so that we may not do otherwise than what we would want to do. So a drug addict may lock himself away so that he cannot fall into temptation, or Martin Luther King may claim that he can do no other than he does and both could claim to have greater free will for it.

There are a buttload of issues for any form of compatibilism, but this debate was pretty dry and I didn't really get here on time. Hopefully this summary is slightly helpful. If anyone's particularly interested I could probably write a load on what it means to be able to have the ability to do otherwise and suggest topic reading, but it's just because this is what I'm writing an essay on this week.