A clause is a group of words that has a subject and a verb.
There are independent and dependent (also known as subordinate) clauses. An independent clause is any phrase that can stand alone as its own sentence. For instance, in the sentence "Sharon and I were shopping when we saw the purse," the first portion "Sharon and I were shopping" would be an independent clause.
A dependent clause, however, doesn't make sense when taken out of the sentence; it is therefore dependent on the sentence as a whole. For instance, "when we saw the purse" would be a dependent clause because it does not have the necessary elements of a sentence that an independent clause has.
Subordinate clauses normally act as single part of speech. They can be either noun clauses, adjective clauses, or adverb clauses.