That like saying it's stupid to cheat on an easy test, some things may be harder for other people. Specifically a trainer has the ability to patch a game file to change gameplay (IE, infinate lives, unlock levels, etc).
To be more exact, a trainer directly modifies memory locations while a program is running to alter something in the game, very much like a gameshark or action replay would. Patches however modify the rom itself.
Very often a trainer will be in the form of a patch which will embed the trainer within the rom! For PC games trainers are most often external programs, yet, for older platforms such as the Amiga, trainers would be put directly in the programs themselves even though they were capable of multitasking... Go figure!