When two frequencies mix, you end up with 4 frequencies.
2 are each fundamental.
1 is the difference between the two fundamentals.
1 is the sum of the two fundamentals.
This mixing of two frequencies is called Heterodyning.
In the case of your CB radio, the crystal frequency is mixed with the received RF in order to create the intermediate frequency which is the difference between the two. If the crystal is 455khz below the rx frequency, the resulting mix creates a difference at 455khz. The next stage filters out the other three frequencies (and all other frequencies around 455khz) leaving only the 455khz RF on the output. This is then amplified and filtered, typically three times total.
Typically you have a bandpass filter, your first RF amplifier, the mixer which creates the 455khz IF (intermediate Frequency) and typically three tunes stages which continue to refine and remove all the other frequencies.
This then goes to a demodulator ( in the case of CB, it's an AM or SSB demodulator) and then the audio amplifier chain and eventually to the speaker.
This type of receiver is called a Superheterodyne and is well explained here:http://www.fas.org/man/dod-101/navy/docs/es310/superhet.htm
In other designs an adjustable oscillator is substituted for the crystal so you can change frequencies in a variable fashion. This is called a VFO or Variable Frequency Oscillator. The rest of the stages remain the same however many modern radios do dual conversion and have two (or more) intermediate frequencies. If I recall correctly, the FCC called for crystal control on CB since VFO designs had been around for decades in the 50's.
Here's another web page that describes the issues with a single IF and why it evolved into a double conversion system:http://users.tpg.com.au/ldbutler/Superhet.htm