In telephone communication, handshaking is the exchange of information between two modems and the resulting agreement about which protocol to use that precedes each telephone connection. You can hear the handshaking in those crunching and other sounds when you make a dial-out call from your computer.
Since the modems at each end of the line may have different capabilities, they need to inform each other and settle on the highest transmission speed they can both use. At higher speeds, the modems have to determine the length of line delays so that echo cancellers can be used properly.
The most common modem standards are briefly described in our V.xx page.