List of all badges with full descriptions
I am not able to understand about some badges and how they are awarded on stackoverflow. Like
Can you please explain me about these badges.
Beta and Precognitive are for people who've been around since the site was on area 51 - precognitive is for people who supported the site pre-release, and beta is for beta testers. They're "If you need to ask, you can't get them" sort of badges
Generalist is a bit tricky - you will need to have gotten a score of 15 (that is to say at least 15 upvotes) for 20 different tags of the 40 highest rated tags on the site - for most sites, clicking the tags button and having the first page's worth of tags (+ 4 more) would give you the top 40, and you need 15 upvotes for regular non wiki answers in half of those.
For cleanup, you'll need to roll back an edit.
For most part you'll end up getting the badges that matter by simply using the site as designed.