A Group is a way to categorize users into convenient sets based on who they are and what types of management you want to have of their internet use.
For example, you may wish to create a Group for the youngest members of your family, and call it "kids." Then you can create settings specific to managing what content the little ones can experience, and when. You could also set up a Group for teens, with different restrictions that apply to those in those wonderful years. You may even wish to create a Group for specific individuals. The possibilities are endless.