to the forums! Pull up a keyboard and stay a while.
And welcome to the hobby!
The Group Build badges (05 or whatever) are badges worn with pride by those people who have taken part in a Group Build. A Group Build is (usually) a time limited, and theme limited common build. Kind of like a contest without any losers! You might have 1 month to 1 year (or even longer) to build, paint and weather a model from a select group or time. The themes can range from, well just about anything. I've seen Group Builds for just about everything: Under 18 yrs, Battle of the Bulge, Thunderbolts, Tigers, Battle for the Atlantic, Pacific Theatre, whatever somebody thinks of and can get other members to go along with. Once a theme has been agreed on, somebody usually creates a bit of artwork that is indicative of the theme and the participants place the artwork in the Signature Field on the Profile page.
See
http://www.finescale.com/FSM/CS/forums/29/ShowForum.aspx for more examples!
I've never been a participant as I'm all over the map model wise (armor-WWII & Korean Aircraft - Hot Rods/Muscle Cars) and have absolutely no discipline regarding schedules! If they ever decide on a "Whatever for However Long Group Build" I am SO in!