ISR - in-synch replicas refers to all the replicated partitions that are completely synced up with the leader.
A replica has to be fully caught up with the leader within a configurable amount of time.
By default, this time is 10 seconds. After this period of time, if a follower is not caught up with the leader, the leader will drop the follower from its ISR and writes will continue on the remaining replicas in the ISR.
If the follower comes back, it will first truncate its log to the last point, which was checked, and then catch up on all the messages after the last checkpoint from the leader.
Only when the follower fully catches up will the leader add it back to the ISR.