As the Jargon File says, an UNIX command for output redirection.
tee(1) is usually used to save the output of a program to a file, while still showing everything on terminal.
Tee reads input from stdin, and writes to stdout and file specified on the command line. GNU version accepts flags -a (--append), that makes the program to append to rather than overwrite the file, and -i (--ignore-interrupts), that makes it to ignore interrupt signals.
It is highly useful for a lot of purposes - for example, to save output of a game. It is very often used as a recorder of Nethack games (many Windows gamers found this program Infinitely Neat and immediately proceeded to install Linux or at least cygwin =)
(Quick guide for Nethackers: nethack | tee -a nethack.out. To replay, cat nethack.out - or, you may try to get some program for sloooow output, such as "slowcat", a program that can be got from my home page, or get the Perl version from Google's Usenet archives =)
There are also some related programs: script(1) and expect(1).