Achievements (for me, at least) are just a reason to spend more time with a game that I enjoy. In most cases, I have trouble enjoying a game if I don’t have goals to work towards (either game-imposed or self-imposed). If I finish the main part of the game, and am not tired of it yet, achievements give me goals that I can follow if I want to keep playing.

Definitely agree that there’s too many games that have achievements that are just in no way worth the time and aren’t even fun as an auxiliary goal, though. The best ones are the ones that get you to do things you otherwise wouldn’t (e.g. playing a non-standard playthrough of the game). The lazy ones (‘Kill X enemies, Earn Y dollars’) are just busywork or earned ‘automatically’ while doing other things and add nothing.