Compatibilism is the view that all human actions are causally determined, while some human actions are free.
David Lewis once said, in a different context, that the most common objection he received was the incredulous stare. That comes up a lot with compatibilism. Understanding compatibilism takes mental discipline. You have to take in the various things compatibilists say, which often seem quite reasonable things to say about human freedom, and keep reminding yourself that compatibilists also think all human actions are determined. (I'll use exclamatory parentheses to help!)
A typical compatibilist strategy is to identify things that seem required for us to act freely, and then argue that, so long as these things are in place when someone performs an action, that action is free. There is disagreement about what these things are. I'll choose some popular ones.
The first is freedom from constraint. A free action must be one in which your body moves as you intend it to. If you are pushed on a bus and bump into someone, or if you twitch in your sleep and tickle someone, we don't tend to think you acted freely. In fact, it's not even really an action--it's just your body moving. On the other hand, if you have freedom from constraint, your body moves because of a decision you made, and so you are the immediate cause of your action. You are able to freely control your body!
(as long as you think free control is consistent with all of your decisions about your body being causally determined!)
Most compatibilists these days think freedom from constraint is not enough for us to act freely. This is because there seem to be cases in which we have freedom from external constraints but we have strong internal constraints that prevent us from acting in the way we really want to. More controversial cases include strong physical addictions and psychological compulsions. Clearer cases include brainwashing or hypnosis. I'm not really sure how hypnosis works, but apparently, someone who is hypnotized does not have the ability to ignore the hypnotic suggestion. We wouldn't want to say that such a person is freely in control of their actions. Contrast this with everyday temptation, where a person can be pulled towards a certain action but resist it through willpower. For this reason, compatibilists often think that to be free, we have to be able to have at least some control over which desires we act on. Some compatibilists think that when we have freedom from constraint along with some ability to pick which desires we act on, we are free!
(even though our choice of which desires we act on is causally determined!)
Susan Wolf argues for an additional requirement for freedom: that we mostly be correct about what's moral. She adds this requirement because she thinks someone raised with perverse moral values shouldn't be held responsible for their actions even if they have freedom from constraint and are able to exert willpower. Such a person would have the ability to revise their character, but not the ability to correct themselves. My analogy for this is being lost in the woods. If you are able to move, you can revise your position. But you need a map and a compass to correct your position. Wolf observes that even if causal determinism is true, someone who has freedom from constraint, some control over their desires, and a (mostly accurate) moral compass can correct their behavior. And if someone can correct their behavior, we can hold them responsible for what they do. What more could we want for freedom?
Well, we might want the real ability to do something other than what we are determined to do. Surprisingly, some compatibilists argue that in fact we do have the ability to do other than what we do, even though all of our actions are determined. They claim that the ability to do something means that if you try to do it, you end up doing it. They then observe that if you had chosen to raise your left hand rather than your right, then you would have ended up doing it; so you had the ability to raise your left hand!
(even though you were causally determined to choose to raise your right hand!)
Compatibilism is custom-made to solve the character problem and the control problem. These were problems for libertarians. If our actions are not determined, how do they relate to our characters and how can they be controlled by us?
For compatibilists, the influence of your character is very clear: when combined with whatever situation you are in, your character (your beliefs, desires, and dispositions) will determine you to act in one way or another. In similar situations, you may act in similar ways. So consistent actions are in no way a challenge to our freedom (as long as you think the causal determination of all of your actions is no threat to your freedom!).
Libertarians face a problem if they model freedom after randomness, because randomness does not allow us to be in control of our actions. Compatibilists have a very clear sense in which we control our actions: if conditions are right, the immediate cause in the deterministic sequence leading up to our actions is us. We are in control of what we do because we are the immediate cause of our actions (even though our characters are ultimately determined by events that happened prior to our births!).
You may be seeing a pattern in the debate about compatibilism.
If you see something more than once, it means they made a gif.
Compatibilists characterize freedom by features of our actions that we in everyday practice associate with freedom and responsibility. Their critics argue that they are missing the true implications of their belief that all of our actions are causally determined. Compatibilists reply by contending that their conditions exhaust everything we might want from freedom. We could keep going, but at this point, we'll leave compatibilists and their critics to sort things out.