Groups are communities where your friends, co-workers, family members, gym buddies, etc. can participate.
It is a community in which you can see a ranking of the members who participate in it, have access to challenges and exclusive rewards.
A group can be public or private. There are groups of communities that everyone can access because they are interested in that community. There are also private groups of gyms or companies, you'll need to have access to participate in them (using a password)
Each group can have it's own challenges and rewards. These are exclusive to members of that group. You can participate in the challenges or redeem those rewards if you have previously joined to the group.