The badge system exists for two reasons:
to teach new users how Stack Exchange works
As the engine grows and evolves, we discover new areas that need badges.
In fact, we've added a bevy of new badges in the last 6 months or so that we haven't had time to talk about yet.
|!(/images/wordpress/analytical-badge.png)||Visited every section of the FAQ|
|!(/images/wordpress/excavator-badge.png)||Edited first post that was inactive for 6 months|
|!(/images/wordpress/archaeologist-badge.png)||Edited 100 posts that were inactive for 6 months|
|!(/images/wordpress/deputy-badge.png)||Achieved a flag weight of 500 by reviewing and flagging appropriately|
|!(/images/wordpress/marshal-badge.png)||Achieved a flag weight of 749 by reviewing and flagging appropriately|
|!(/images/wordpress/proofreader-badge.png)||Approved or rejected 100 [suggested edits](http://blog.stackoverflow.com/2011/02/suggested-edits-and-edit-review/)|
|!(/images/wordpress/synonymizer-badge.png)||First approved [tag synonym](http://blog.stackoverflow.com/2010/08/tag-folksonomy-and-tag-synonyms/)|
|!(/images/wordpress/tag-editor-badge.png)||First [tag wiki edit](http://blog.stackoverflow.com/2010/08/new-tag-info-pages/)|
|!(/images/wordpress/vox-populi-badge.png)||Used the maximum [40 votes in a day](http://blog.stackoverflow.com/2011/05/vote-for-this-question-or-the-kitten-gets-it/)|
|!(/images/wordpress/quorum-badge.png)||One post with score of 2 [on meta](http://blog.stackoverflow.com/2010/07/new-per-site-metas/)|
|!(/images/wordpress/convention-badge.png)||10 posts with score of 2 [on meta](http://blog.stackoverflow.com/2010/07/new-per-site-metas/)|
Badges are supposed to be a little mysterious; you should view them as minor puzzles with obvious hints.
What activity is this badge referring to?
How do I perform this activity?
Why is this activity important and necessary?
Who should normally perform this activity, and when?
Most of these are fairly self-explanatory, but I believe the flag weight and review sections do warrant some background. Of course there's the insanely detailed meta faq about flag weight, but the short version is this: flag things that community moderators agree is helpful, and your flag weight will go up.
Your flag weight, if it is something other than the default of 100, will be visible on your user profile under your reputation score.
You can view the status of your flags by clicking the flag weight link. There are two flag dispositions, helpful and declined. Generally, so long as you are flagging in a genuinely useful manner that helps make the site better, most of your flags should be of the former and not the latter.
If you're looking for posts to flag -- or vote, edit, and comment on -- I highly recommend using the review link on the site. At the top of every page you'll see one of two links: either review (from 200 to 9,999 reputation) or tools (from 10,000+ reputation and beyond). Both can get you to the review page.
Click around on the review page and read the explanation on the sidebar to get the gist of it.
Please do bear in mind that flagging is no substitute for the normal editing and voting process. We encourage responsible flagging, but if a question should be closed, or a post downvoted, don't hesitate to take action yourself. Actions from the broader community as a whole speak much louder than actions from community moderators!