PBEM (Play by E-Mail) is one of the two ways you can play over a modem or a network. It is most suitable for "turn based" games like Capture the Flag. The first person makes all of his moves and then at the end of his turn saves the game in the PBEM format. Then he transfers this "saved game" to his opponent.
The most common methods for transferring are attaching the "saved game" to a email message to his opponent or, if he's on the same network, by moving the "save game" file to a drive where his opponent can access it. If you're on the Internet you can also FTP the game to your opponent. If you're not on the Internet but using a modem you can also upload the "saved game" to your opponent.
Once his opponent receives the game the opponent plays his turn. When he finishes his turn he then sends the "saved game" back by repeating the above process.
This is a great way to play with friends around the world without tying up your phone.