An appositive phrase is a noun or a noun phrase that renames, identifies or gives further information of another noun right beside it. Now, this type of phrase can be either restrictive or nonrestrictive (when it's not essential to the sentence, and therefore should be set off with a type of punctuation).
The type of punctuation used in nonessential or nonrestrictive appositive phrases are commas, dashes or brackets. Here are some examples:
Mariana -that girl with the red jacket- is not from here.
My cat, Tigor, does not eat fish.
I need to clean up those shoes (The ones with the red bow).