Sponge is a solid.
Still it can be compressed, this is due to the presence of minute pores all over its body. Air is present in sponge because of these pores, increasing its over all volume.
When we squeeze the sponge, all the air inside in is expelled out and the sponge shrinks in size , enabling us to compress it.
Once released , air rushes in the holes once again.
How ever it's not possible to compress a sponge once all air has been expelled from it.