In classical physics mass is a measure of inertia. Similarly in QFT the effect of mass is to slow down the speed at which a field evolves and propagates, so mass plays the same inertial role in QFT as it does in classical physics. But this is not all that mass does. This same term also causes the field to oscillate, and the greater the mass, the higher the frequency … the energy of a quantum is represented by oscillations in its field intensity: the more energy, the faster the oscillations.
