When you look at someone's profile, right next to their name it says something about groups. What is this all about? Is this the aircraft clubs in the community pull-down?

Some people are members, others are moderators or administrators. This would let you know the difference.

like here:
http://www.rcuniverse.com/forum/show...sp?memid=22607
When you click "group membership" It says "this person is not in any user group"
What does this mean?

Look under my profile and I think you will gain a better understanding of this concept. Basically, it's more useful for the administrators than it is for the members.

How do you become a member of a group?

Groups are defined for RCU management to organize the heirarchy. Look at your profile and click the group link and you'll see you belong to the moderator group.