The Mixer

When two frequencies are mixed together, a third, 'beat' frequency is created which is actually the difference between the first two. By mixing the incoming radio frequency wave with a locally-generated wave, a third frequency is created. Now, (here's the clever bit) if the locally-generated wave changes frequency to 'track' the incoming radio frequencies, the beat frequency (the output frequency) is always the same.

By convention, it's arranged so that the output frequency is always exactly 10.7 MHz. If you want to receive a higher radio frequency, you increase the frequency of the local oscillator so the output is still at 10.7 MHz and vice versa.

So now, regardless of the frequency we wish to receive at the antenna, we are always dealing with a frequency of 10.7 MHz and building very narrow, high-gain filters for a single, relatively low, frequency is easy.