A group is a customizable database of contacts that can be private or shared. You can create as many groups as you want directly from the sidebar.
Groups can be private or shared. You can control who has access by using the "Share" button on the top left. When you create a group, it is, by default, a private group (only visible to you).
You can bookmark you favorite groups so they don't get buried into your sidebar. Just click "Add to favorites" and pin it to the top of your sidebar.