Compatibilism is the belief that there is no conflict between the ideas of free will and determinism. In other words, it is possible for all our actions to be determined by natural forces, and for us to have a meaningfully free will. They base this belief on a particular definition of "free will" -- to them, an action is "free" if it is not forced upon a person by compulsion outside the actor. When an act is caused solely physical causes but is not coerced, compatibilists conclude that the action was both "free" and "determined." Compatabilists argue that the issue is one of perception rather than reality. Christian Compatibilists, for example, say God does indeed know past, present and future, because he knows what path someone will take since it is built into that person's identity. But to the individual making the choice, it appears as if it is totally free -- therefore, it is.
Incompatibilists, by contrast, define an action as "free" if it is independent of prior physical cause, and conclude that if everything has a physical cause, then nothing is free, and therefore that free will and determinism are incompatible.