What is a task group?
Think of a task group as a category. They let you assign granular tasks that are similar into a parent category, like "Design" or "Home Page".
I might have a project that has tasks like, "A user should be able to upload an avatar photo", "A user should be able to set their bio", etc. and all of these would probably appear in a task group titled "User Profile Page".
From the "Groups" tab, you can see quick statistics about each task group — How complete is it? How many outstanding tasks exist in it? How many hours has been logged for this group? You can also discuss each task group like you would a task by clicking through to it.