There are a couple groups already. see: alpha.glitch.com/groups/
I went ahead and created a PARP group... I'll happily give up administrator to whoever wants it.
There will likely be many tens of thousands of groups one day.
And they will have discussion boards, yes, but mostly (we think) they will be used for group-based ownership of things (locations, say, or shared bank accounts, or whatever) in various different configurations (co-ops, corporations, religions, political parties, guilds, alliances, secret societies, etc.)
Groups will be able to collect money from members (think of protection money, membership fees or tithes) or, conversely, pay salaries to members in exchange for their labor. They are as hierarchical as the creator wants them and each level can have it's own permissions (promote/demote, kick/ban, invite, etc.)