The easiest way to think about it is this...horse power is the result of combustion. You burn gas, which creates heat, which creates expansion, which moves pistols, which turns a crank, which spins a fly wheel, etc. A small burst of flame does this. The larger the flame, the greater the power. BUT! You can only burn as much gas as you have oxygen in the chamber. No oxygen, no flame. So, you can make the combustion chamber larger (stroking, increasing displacement, etc), Or you can force more oxygen into the cylinder at the point of combustion (forced induction). More oxygen, more fuel can be burnt, bigger explosion of flame, more violent expansion pushing the piston, more power.
Also more stress on the motor, which has to contain the force of that explosion.
Increasing power is simple. Increase the psi of the boost, which allows you to burn more fuel, which creates a larger explosion. Surviving that...is the challenge. Building an engine isn't so much about creating horse power, but about making an engine tough enough to survive the creation of that power (larger explosions).
