A group allows members that you've grown close to on B.Net to have a little space separated from the general hustle and bustle. It gives you access to databases to share information. Contact info for other means of communication, and a few other various and sundry Knick-Knacks.
As far as advantage over anything -- that's hard to measure specifically, as some people enjoy being a part of a group, and some people don't. Most group founders like you to be at least a little active, and sometimes people just don't have the time. Groups are mainly for extra socialization, and it's just our own little slice of Bungie.
You can find a few groups in the Group Directory Sticky in the Classifieds, that I'm sure you could look at and make your own judgements about.
By the way, Welcome to Bungie! since this is your first day - Make sure all your posts are in the relevant Forums. Since you are this new, I'll make a blind assumption that you're here for Halo and Halo 2, which are The Library and New Mombasa respectively. Group queries can of course be made here, and adverts go into the Classifieds. For Off-Topic General discussion, visit - The Flood.
Have a great day!