An Americanization of the word "mecha", which is itself a Japanese-ification of the word "mechanical". A mech, or 'mech, or mecha is basically the same thing as a giant robot, with the exception that a mech is almost always piloted. In other words, it is a large mechanical vehicle of (sometimes very vaguely) humanoid form.

Besides the examples Hai-Etlik gives, I would point out that Macross, Neon Genesis Evangelion, The Vision of Escaflowne, and Gunbuster, among many others, also feature mecha.