SuperHeterodyne receiver
Take a Frequency Modulated (FM) signal going into a superheterodyne receiver which has a tuning range over 88 to 108 MHz.

Any given FM signal will occupy a much narrower bandwidth than that. Typically an audio signal will deviate the carrier, that is modulate the frequency, by around +/- 100 kHz. If we take the carrier to be 95 MHz, then the complete signal is represented by the frequency changing from 94.9 MHz to 95.1 MHz.

Let's say we have an Intermediate Frequency (IF) of 10.7 MHz, this is the frequency almost invariably used in commercial FM receivers. The IF could be another frequency in that ballpark, but 10.7 MHz has been settled on as a de facto standard, and there are a lot of cheap components made and used for that frequency.

To 'tune to' our 95 MHz signal, the first Local oscillator (LO) is set to 105.7 MHz. We mix the incoming signal and the first LO, and our IF filter picks out the difference frequency, and signals near to the difference. Typically the IF filter has a bandwidth of a few hundred kHz, to cope with the full width of the frequency deviation, and a bit more. 95 MHz translates to 10.7 MHz. 95.1 MHz translates to 10.6 MHz, and 94.9 MHz becomes 10.8 MHz. All of those signals pass through the IF filter.

So at the IF, just as at the carrier, we have a frequency modulation. It's the same rate and same deviation, and represents exactly the same information. 

By setting the first LO to other frequencies, we can get other carrier frequencies to pass through the IF filter. Perhaps the most important part of the filter is that nearby RF frequencies do not pass through the IF filter.

Once down to a fixed frequency range, we can build a high quality FM demodulator, that maps the changes in frequency around 10.7 MHz into changes in voltage, to recover the modulation. Most demodulators are designed to only accept the specific frequencies passing through the IF filter, so all tuning is done by changing the LO frequency.

It's the signal bandwidth that determines how much information can be carried, not the signal centre frequency. The 95 MHz version and the 10.7 MHz version of a standard audio FM signal carry the same amount of information. However, with a higher centre frequency, it's possible to make a signal with a wider bandwidth. So for instance if you wanted to make a 25 MHz bandwidth signal, that's not physically possible at a 10 MHz centre frequency, though is perfectly possible at 95 MHz centre.