While there are a lot of names for this control, the talkback function is a useful tool for you to monitor your own transmissions. In radios that do not have talkback, you are unable to hear your voice through your speaker. Which means if your radio isn't transmitting, you may not know it. Talkback allows you to hear yourself, which tells you that your radio is probably transmitting.
Why would I want to hear myself?
This control is very similar (hence the sometimes used name of Monitor) to the monitor systems that professional singers use, by monitoring their voices, they can make sure they're singing correctly. While you may not be singing on your CB, it's still useful to know that your radio is modulating to some degree. The other reason you'll find talkback on any radio is due to an effect known as echo. Echo boards are an add-on modification for CB radios, and thus will not be found inside a radio unless it's been added to it. Some CB microphones will provide an echo effect as well. Having talkback on your radio (or T Back as cobra calls it) will allow you to hear the echo yourself, so you can get the echo set where you think it sounds best.
Stop making that sound! Talkback and squealing.
The benefits of talkback are almost entirely limited to a) monitoring your radio to make sure it's working and b) adjusting your echo board (if it's present). If your talkback is squealing / screaming / screaching -- generally making not good sounds, refer to this chart for common ways to resolve it: