well basically this is what it does:
say you have a user which is in the "Registered users" group with the normal "number-of-posts" related rank. Say this same user is also a member of other 3 groups each one having a rank and an image associated to that rank.
Then, on every post of the user you will see the ordinary "number-of-posts" related user's rank image followed by the three images of the three ranks of the three groups the user is in. In this way if you want a user (or several users) to have a specific rank, other than their normal one, you can create a group with a special rank and make the user or the users members of that group.
You can also try MODs which automatically move users in groups according to their posting activity in order to give them special addictional ranks.
Of course every addictional rank you want to give to your users requires to have a specific group set up with its rank and rank's image. But in this way you can have and manage multiple ranks by only using odrinary phpBB3 groups management functions and without any database change.