What information does the appositive phrase provide for the reader? Most people are familiar with asterism's, informal constellation names such as the Big Dipper

The appositive phrase defines the term asterism. It tells the reader that an asterism is an "informal constellation name".

Appositive phrases are often surrounded by commas. They follow a noun and rename or describe it. Another example is "My dog, a yellow lab, loves to play ball." In this sentence the appositive phrase is "a yellow lab". It describes the noun - dog using a noun - lab.