Achievements are a way of recording progress through a game. They can provide challenges and act as 'medals', I mean who wouldn't want a medal saying 'I killed a dragon with my bare fists!'
Yeah, but really they mean nothing to the individual - if anything, they're bragging rights. I sometimes will go out of my way to do something outlined in one, if it's funny, like in Fallout 3 there was, I believe, Pyrotechnic Pickpocket, for putting an explosive into someone's pocket through pickpocketing. That is something I would not have done otherwise - probably wouldn't have known you could do, as there is nothing saying you can do so (wouldn't have thought pickpocketing would let you put a live grenade on someone). Glad it was there.
Actually, really hope the achievements/trophies/whatever Steam has are really well done this time. I'd like to see some real challenges/things you can't do in one playthrough. I don't *need* them, but if they're done right they do add enjoyment (for me).
Oblivion's were pretty much crap, though. Go through this guild, arena, MQ... meh.