The license manager (Armadillo) checks the local network for overuse of the key. You can use ClipMate on as many machines as you've licensed it for, plus one more (to allow for a laptop, for example).
If you exceed the licensing, then you will need to either purchase additional licenses, or uninstall ClipMate on some stations.
Note that if you can mix and match licenses. If you have a 10-user license and need to add 5 more seats, you can either get a new key for 15 users, or get a new one for 5 users and use it on 5 new stations, and the old 10-user key on the original 10. You can have any mixture of licenses, as long as you don't exceed the total by more than one.