on January 28, 2012
at 03:48 AM
Some of them you can just figure it out.
Example: You have 5 Nice Answer badges. A Nice Answer is defined as being voted up 10 times. So look at your answers sorted by "votes" and see which five have upvotes of 10 or more.
For other badges such as Commentator (leaving 10 comments), I don't think there's any way to see which are the first 10 questions you commented on.
on January 27, 2012
at 11:06 PM
Click on your profile name (next to the envelope), scroll down to "Answers" and click the "recent" link. The badge is likely related to something at the top of that list with 10 or 25 rep votes.