It's actually standard UNIX quota soft/hard limits. So you have a soft limit of your (paid quota) that you can drift above for 7 days (that is the grace period) and you have a hard limit of (quota * 1.1) that is ... a hard limit.

We have an automated alerting system that emails primary and technical contacts in a progressively more aggressive fashion as you drift above the soft limit and approach the hard limit...

The grace period is probably quota recalculation if it's not done natively by the fileserver. If it's only a periodic count then you could potentially get higher than 10% before you're cut off.