The theory is that there is a mass of solid iron-nickel, as described in some previous answers. No one has actually been there, of course, to confirm this, but the evidence is pretty solid (no pun intended).
Branman... is right. It is a solid core with a liquid mostly iron core surrounding it. I have heard an interesting theory that Uranium is so heavy that it is very concentrated in the core and accounts for much of the heat allowing our planets active geology. It could be there is a nuclear pile or reactor of sorts at the core.