A dependent adjective clause is a group of words containing a subject and a verb. It offers further description or information - similar to what an adjective does - about something that was mentioned in another sentence. Adjective clauses are often introduced by relative pronouns such as who, which, or that.
In the sentence we are analyzing here, the clause "who bought me a puppy for my birthday" offers further information about "the one" - and "the one" refers to "my uncle".
The subordinate clause in this sentence is "who bought me a puppy for my birthday" and it functions as an adjective because it modifies the noun phrase "the one" (like adjectives and adjective phrases, adjective clauses describe or add information about a noun element in the sentence).
