Probably the principal of her school (head teacher in the UK). I don't know whether the principal was mentioned previously or whether she uses the principal (and by extension his or her daughters) as a model of the respectability to which she aspired.
I thought it was possible that she hadn't mentioned the principal before. When speaking of childhood or school days the principal would be a well-known or standard figure or respectability, I think, and wouldn't necessarily need any special introduction.
A principal in the U.S. is the administrator of a school. Normally, principals must posess teaching certificates as well as administrative certificates. They normally earn more than the rest of the teaching staff, often because they work more days.
In a very, very small school, he/she might teach a class as well.
Obviously, Tina did not feel compelled to mention the principal's name.