i'll explain using more layman terms 
imagine air as tiny particles with lots of space between each
particle.
now, when pressure is exerted over a fixed vol of air, the spaces
between each particle gets lesser, and the average rate at which
they are colliding into each other within a smaller space
increases.
such "collisions" increase the kinetic energy of the air particles
and they heat up as such.
as air heats up, the particles try to distant themselves again to
achieve equilibrium, and therefore, they expand.
hence, if such compression/expansion were allowed to happen as it
is, the engine would receive less denser air if the heated air
passing thru the turbocharger does not get get a chance to become
"denser" by allowing it 2 pass thru a intermediate heat transfer
agent such as an intercooler, which helps to "stabalize" the
movement of the air particles by taking away some of their kinetic
energy. voila! more air particles per unit time reaches the engine.
