Actually speaking
Convolution is one way of predicting the response of a LTI system When it's impulse response is known to us

In other words If you know the impulse response of any Linear Time Invariant System h(t), Then you can easily find out what will be the output of the system with input f(t).

Lets take a modulator having input f(t)

Here the impulse response of the modulator will be h(t) and so the output of the modulator for the input f(t) will be given by the convolution of both the signals