what exactly is a trainer? what does it do? and, my guess is, it's a bad thing... right?

It generally means a program that lets you cheat. They usually modify the memory of the game, giving you unlimited ammo, unlimited health, move you around the map, etc.

They are not all bad though. For example, programs like Project Cataclysm, Project Controller, ChatLogJJ2, and Admin Kit Server are all good trainers.