Angel in training is the term used for Angels who are in training to become full Angels. Angels that are in training are given an Human assignment to look after before they can become a full Angel. There assignment can be to make their Human more popular (Porter) or to save a Human life (Lou).
It was revealed in "Lucy in the Sky with Carl" that Angels in training are required to take a Human test before they are allowed to beam down to Earth. This test is shown to be part of a class which is taught by Angel who knows very little about Humans and who admits that he only ever read about them.
Whilst AITs are on Earth completing their task in order to become a full Angel they are assigned a supervisor to watch/ help them out. Dr. Cassabi is the supervisor who is assigned to look after Porter and then Denise.