We really don't know. There's a lot of theories but nothing confirmed.

The commonly accepted theory these days is a rocky metallic core (mostly iron/nickel), like the inner planets. But right above it is basically an ocean of liquid metallic hydrogen. Heat and pressure are essentially opposing forces when it comes to what state matter will take. Heat pushes the element toward gas, pressure pushes it toward solid. In the center of planets like Jupiter the pressure wins, hence the liquid hydrogen ocean. The only reason we don't think there's solid hydrogen there is that there isn't enough pressure for hydrogen to solidify at the temperatures in Jupiter's core.

Note that gas giants can get big. There's been some that we've seen that are borderline stars. If they got just a little bit more matter they would have enough gravity, and therefore pressure, to kick off fusion and turn the core into plasma from the heat.