The problem of free will arises from a collision between two powerful intuitions. The first: the laws of nature are deterministic (or, in quantum mechanics, probabilistic but still not under your control). Every physical event is the product of prior physical causes. Your brain is a physical system — therefore your decisions are the products of prior causes, not the free initiations of an uncaused will. You are, on this view, a very complicated domino.
The second intuition: it feels, from the inside, as if you genuinely choose. The experience of deliberation — weighing options, feeling the pull of different possibilities, and then deciding — seems to be the experience of genuine agency. When you choose to lift your hand, it feels as if you could have chosen not to. This experience of agency is so fundamental that even those who intellectually accept determinism cannot help acting as if they are free.
The tension between these intuitions is the free will problem. If determinism is true, the experience of choice is an illusion — elaborate but ultimately empty. If libertarian free will is true, there must be something in the causal chain that is not determined by prior physical causes — and it is not clear what that could be without invoking something supernatural. The debate has been ongoing for centuries and remains genuinely unresolved.