The other post give good examples, here is another.
Image a Discourse site for use with high schools around the country that have teams competing in a national competition such as FIRST ® Robotics Competition. (ref) Now instead of each team having to spend time setting up a communication channel, they all join a single Discourse site. To keep the individual teams from seeing the details of other teams, each team is put into a group and the group is given a separate category for posting only visible to that group.
But users can also be in more than one group, lets say school district and state. So these could also have a category for them. Also if a category is not tied to a group then everyone can join in.
Make sense?