a·chieve·ment - n.
1. The act of accomplishing or finishing.
2. Something accomplished successfully, especially by means of exertion, skill, practice, or perseverance.
The achievement system was introduced back just before the launch of Wrath of the Lich King. There wasn't really any purpose to the achievement system, although some achievements give pets, items, or titles -- the main purpose of an achievement seems to be just... something to do when you've got nothing else in mind.
Personally, I love the achievement system. I like being able to plug away at something tedious and somewhat mind numbing every now and again, regardless of the fact that those points really don't mean anything. What bothers me though, and has bothered me since the first cries of an achievement being too difficult to complete is the little voice in the back of my mind that wonders if people realize what an achievement is supposed to be.