time domain multiplication is frequency domain convolution. Which is great if you want to shift the frequency band of some signal. Like if you have 2 songs that you want to play over radio in the same, shared airspace, you shift them to two different frequency bands. This happens electrically/RF-ly as a multiplication.

I know this, but how does it relate to resonance in physical systems?

E.g. imagine a rigid pendulum driven by a sinusoidal torque at its pivot point. Which signals are multiplied here??

Mixers are physical systems. The precise words for the distinction you are trying to make is between linear and non linear systems.