When I go online, the computer always says something about the modem "handshaking" som...

In order for data to be transmitted over the Internet, the modems on either end of the connection must be in sync, and agree on such parameters as a speed with which to exchange the data. For example, if one modem transmitted data at 28.8 kilobytes per second, and the other one only supported up to 14.4 kilobytes per second, those two modems would have to agree to exchange data at a speed that was accessible to both -- in this case 14.4 kilobytes per second would be the highest common denominator. The handshaking process occurs when the two modems detect each other over the Internet, and adjust themselves within parameters that both of them can handle.