This question came to us with a specific example, wondering about the correct punctuation in this sentence: The eleven-inch wand, the one made of ash[,] shot out a stream of sparks.
Let's start by identifying "the one made of ash" as an appositive phrase. Our Grammar 101: Prepositions & Phrases
article defines an appositive as "a noun or pronoun, often with modifiers, that renames or identifies another
noun or pronoun within a sentence." ( Punctuating Appositives with help from Harry Potter and Buffy the Vampire Slayer )