Yep spot on.
Because the air is compressed by the turbocharger, it heats up, therefore it becomes less dense - the molecules are further apart, so can fit less inside the cylinder, so cooling it back down makes the charge air denser, which means molecules closer together, therefore more oxygen in a given space, therefore can burn more fuel with the larger quantity of oxygen, thus more torks, thus more powahz.
Because the air is compressed by the turbocharger, it heats up, therefore it becomes less dense - the molecules are further apart, so can fit less inside the cylinder, so cooling it back down makes the charge air denser, which means molecules closer together, therefore more oxygen in a given space, therefore can burn more fuel with the larger quantity of oxygen, thus more torks, thus more powahz.