So we've done participles and gerunds, and because @glamAtude asked whether we could talk about appositives, here we go:
An appositive is a word or phrase that follows a noun and gives more information about it.
It can be a single noun: Her new puppy, Paperboy, came home yesterday.
It can be a noun phrase: Paperboy, her new puppy, came home yesterday.
It can be a noun phrase plus a prepositional phrase: Her new puppy, a black-and-white ball of energy, came home yesterday. Her new puppy, a mutt from the pound, came home yesterday.
And so on. You can take out the appositive and you'll still have a complete sentence.
Relative clauses are not the same as appositives, though they may convey the same information. Relative clauses begin with a relative pronoun and have a verb in the clause. Appositives are simple phrases, no verb. Relative clause: Betty, who is my neighbor, said … Appositive: Betty, my neighbor, said …
Usually appositives are set off with commas (one before and one after), because they're adding extra information about the noun. These are called "non-essential" or "non-restrictive" appositives.
But sometimes an appositive is necessary to set apart or distinguish the noun: Paul Simon the senator (as opposed to Paul Simon the singer) Her dog Paperboy (as opposed to her dog Scout)
These are called "essential" or "restrictive" appositives, and are not set off with commas.
A note on agreement: The verb agrees with the main noun, not the appositive. Truffles (plural), a luxury food (singular), are (plural) … Paperboy (singular), one of the nicest dogs (plural) at the pound, is (singular) …