The speaker's voice (yours) is combined with the receive audio path so that you get the comforting sound of your own voice feeding back along with the incoming audio, particularly when you have headphones on - sort of similar idea to the fold-back that musicians use on stage. Probably stops you from speaking too loudly - as I tend to do when I speak while wearing hearing protection.
Sidetone is also used on telephones. At least it once was in the old days. I guess it still is.
Some people also refer to subtone or sub-audible tone systems as sidetone.
If that is what you are refering to, it is a form of selective call or tone squelch system
A frequency below the normal speech band is added at the transmitter, say 67Hz.
The receiver only enables the audio (or opens the squelch) if it detects that specific frequency in the receive audio.
This allows different users to share a radio channel without hearing each other's conversations.