It all has to do with molecular spacing in a substance. CO2 gas is a gas and has a larger inter-molecular spacing and these molecules can be pushed around to compress the gas (which will reduce the inter-molecular spacing). On the other hand, dry ice is solid CO2 and has much less inter-molecular spacing and further compression is not possible and hence is termed incompressible.
According to kinetic-molecular theory, in gaseous phase, molecules are in constant, random motion throughout (mostly) empty space and hence can be pushed into smaller volumes; i.e. compressed. In solid phase, molecules are very tightly packed and they can only vibrate or oscillate about fixed sites. This makes further compression difficult. For example, we can take 4 marbles in a small glass jar and moves them around as much as we want (by swirling). If, on the other hand, we fill the jar completely with marbles, the motion of marbles become very restricted due to lack of free space. Gases and solids are exactly like that.
Hope this helps.