How do I create a group for tournament invitations?

Go to Account → Connections → Groups. Click Create group, give it a name (and optionally a description and filters like level or gender). Then add members by searching for players from your connections and adding them to the group. Save the group. When you open Invite players on a tournament, your groups will appear; select one or more groups and the matching members are added to the list before you send the invitations.