Clauses come in two varieties: independent and dependent. A dependent clause cannot stand by itself as a sentence. Dependent clauses will act in one of three ways in your sentences: (1) adjectives, (2) adverbs, or (3) nouns. An adjectival clause modifies a noun or pronoun; an adverbial clause modifies a verb or sometimes an entire sentence; and a noun clause substitutes for, and performs the grammatical functions of, a noun. Examples of each follow:
That she won the race did not surprise us. (noun clause acting as the subject of the sentence).
He left the party because he was tired. (adverbial clause modifying the verb left).
He enjoyed the party, which lasted all night. (adjectival clause modifying the noun party).