Family Browser R3 uses a floating license model. You are able to install Family Browser on as many computers as you like but you will only be able to use Family Browser on as many computers at once as your subscription allows.
A family browser license is checked out of the license pool when you start up Revit and is returned to the pool when you close Revit. This requires an internet connection. On a single computer you can have multiple versions of Revit running at once, ie Revit 2019 & 2020, and that will only check out one license.
If for some reason there is no internet connection or there is a failure to connect to our license server there is a 2 day grace period from the last successful activation that Family Browser will still work.