Grammatically speaking, “appositive” is a fancy word for “equivalent.” For example, when we refer to your dog Smurf, “Smurf” and “your dog” are appositives—the same thing (or animal, in this case) restated in different words.
And we know that Smurf can’t be your only dog, because the name isn’t preceded by a comma. Add one—“your dog, Smurf”—and it’s now clear that you have just the one dog.
Or is it?
Meaning isn’t determined by commas alone; it also depends on context. Moreover, of the two, context is usually the more important consideration; commas merely work in support of context. And that means commas aren’t always strictly necessary, even when you think they might be.