Solvent: A substance that dissolves a solute (a chemically different liquid, solid or gas), resulting in a solution. Like the water you're trying to soak into the sponge.
Solute: A substance dissolved in another substance. Like the dirt particles in your water that get trapped in the sponge's pores.
Supersaturation: A state of a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances. It's like squeezing extra water into your already soaked sponge by applying pressure.