Active Replication is the replication between application's objects. That is obviously can be used to build fault-tolerant applications, normally real-time (like patient status tracking in hospital, or starship launching ;-) ) where importance of correct functioning is huge.
Active replication is the mean to guarantee that in case of a single object failuire the application can recover and use another object without loosing any data, or producing incorrect result. "Active Directory Replication" is performed with similar goals, but this is just a small example of how fault tolerance strategy can be implemented. And "Active Directory Replication" serves other purposes ("not fault-tolerance") as well.