The mixer has two input signals of different frequencies, f1 and f2.
These inputs are mixed together in the mixer. (some books say "beaten" together, others say "heterodyned").
f1 and f2 then come out of the mixer, together with two new frequencies.
One of the new frequencies is the sum of the two inputs, f1 + f2.
The other is the difference between the two inputs, f1 - f2.
For example, if the inputs are 1 Mhz and 1.47 MHz then the sum frequency is 2.47 MHz. The difference frequency is 0.47 MHz (470 kHz).
Sometimes, on the radio, two adjacent stations will produce an interfering whistle. This is because their frequencies are close enough to beat together. The difference between their frequencies is in the audio range.
If you have two racks of equipment, cooled by fans, the noise produced by each fan rotating often beats together to give a low frequency beat noise.
Mixers are used as part of the FREQUENCY CHANGER in radios. Understanding
mixers will help you to understand the MODULATION process in A.M. transmitters.