The appositive phrase that is present in the sentence "My advisor, Mr. Burns, is helping me apply for scholarships specific to students who major in astronomy, the study of the universe" is "the study of the universe".
An appositive phrase includes an appositive, which can be a noun or a pronoun, and its modifiers. Furthermore, "the study of the universe" is an example of nonessential appositive phrase, which means that the phrase provides additional information about the noun that is modifying ("astronomy"). In other words, in this case, the appositive phrase is not necessary to identify the noun that precedes it. The phrase is only making the sentence more detailed.