Hello I am relatively to Stack Exchange and I was wondering what are badges for? Do they give you privileges reputation, or are they just another thing to get more of?
As Steve pointed out badges are more or less for fun and bragging only. There is however one opportunity where certain badges might carry some weight, and that is moderator elections. While the candidates should make their point beside reputation and badges, e.g. by means of the questionaire, some badges relavant to moderation are listed during the election period too. For those voters who don't want to read all the stuff, rep and badges might be some kind of a guide. (Again, some it is, or at least that is what I hope. It should not be about the numbers only.)
So of you intend to run for moderator in the future, collect some badges that show you're also up to the house keeping work that comes with it, e.g. voting, flagging, editing.
Here's how the candidate score is calculated.
Badges do not grant you privilege. Privileges are tied to reputation. Badges are however, part of the gamification of all the stackexchange sites. So they carry bragging rights only. Most questions about reputation, privileges and badges can be answered by reading the site's help documentation.