An abbess is the leader of a monastery, with many nuns in their charge, it is their duty to oversee the vows taken and then adhered too. Monastery rules vary by region, but common rules are the presence of the abbess to lead morning prayer, to thank their lord before meals and greet guests.
Abbesses are chosen by rank, when one passes, the next highest rank becomes the abbess as they are deemed to be the wisest of them. Nuns determine their hierarchy by the time spent within individual monasteries, it is common to say that no nun will know more about the monastery than the abbess.