The appositive is a part of the sentence giving additional information about a noun present in the sentence. To recognize if a word or phrase is an appositive you can do the following:
Try reading the sentence skipping the phrase. If it makes sence then the phrase is the appositive.
Here the appositive is "Ms. Carlton". It describes the subject My teacher. If you skip it you get:
My teacher wants to become principal
The sentence is still correct, so the phrase is an appositive.