The term Mech comes from the word mechanized. The most widely known use of the term mech is the BattleMech from FASA's Battletech. Likewise the tech mecha came from Robotech.
Mechs can take many forms, but a general discription would be a large roughly human shaped robot, with a human pilot. In the case Battletech and Robotech, mech are about four stories tall, wear tough armor and carrier massive fire power. The Mobil Suits of the Gundam series are the same, were as the Eva's of the Evangleon series are twice that size and are mainly melee fighters