The matter in which the atoms have large distances is considered as compressible matter. The atoms of gas have very large distances and they have much capacity to be compressed. Atoms of liquids are arranged at relatively lower distances as compare to gas atoms. Therefore, liquids cannot be compressed in terms of their volume but their shape is changed with the change in vessel. However, most of the solids have very packed arrangement of atoms and thus, they are incompressible. In the case of solid and gas like foam which has pores, you can compress it. One example of it is that you can compress air in a pressure cooker but you cannot reduce the volume of wood by compression.
