An example of an appositive is: my brother, Jeff, is outside. Jeff is the appositive. Appositives are nouns or noun phrases that are located next to another noun and are used to identify or describe the noun.
Another example of an appositive is: Jeff, a hot headed hockey player, started a fight with the goalie after being tripped. In this sentence, Jeff is the noun and "a hot headed hockey player" is the appositive, which gives more information about the noun.
Appositives can be short or long and will generally follow the noun it explains, but it can also precede it in a sentence. Sometimes a noun in a sentence is too general and the information contain within the appositive is necessary e.g., The popular teacher Mr. Jones was known for his jokes and puns. In this sentence, no commas are used around the appositive because it is essential information.
In other sentences, the appositive does not add necessary clarity to a sentence, for instance, in the following sentence. During breakfast, John, the loudest member of the family, got in trouble for interrupting mom's story. John being the loudest member of the family is not essential information in this sentence, and the sentence would still be clear without it, so it is separated from the rest of the sentence inside of commas.