Many of these abbreviations come from CW (see below!) operating, especially in the early days of amateur radio. Just as in the early days of texting on a mobile phone without word completion, shorthand was used.

CQ Letters used by an operator when calling and looking for a contact with another radio amateur.
CW Continuous Wave - more familiarly known as Morse. It's not really continuous wave, since you have to break it up into the dahs and dits to communicate information.
DX Distance communication. This can mean around the World, across the Atlantic, or just across the Irish Sea, depending on the frequency band and so on being used.
FM Frequency modulation. Popular in handheld radios, but greedy on the batteries, since when transmitting a full power signal is transmitted all the time.
OM Old man. Any (male) radio amateur.
Operator The person operating the amateur radio station.
SSB Single sideband. Popular for voice DX communication, since it's economical with the power; if there's no sound, there's no signal!
XYL Normally used to mean the (male) operator's wife. Don't often hear of an XYM ... but then there are not as many YL operators as there should be.
YL Young lady