Ok, I don't like the way they explained Clauses, so I'm going to attempt to explain it myself. A clause is basically a set of words containing a subject and a verb. (sometimes the subject is implied.) There are two types of clauses; An Independent Clause, and a Dependent Clause.
Independent Clauses
Independent Clauses contain all of the information necessary to make a sentence, and are capable of standing on their own.
Ex.
Terry ate an apple.
In this example, the clause made a complete statement, and thus, would be considered independent.
Dependent Clauses
Dependent Clauses are lacking in some way of the necessary information to make a sentence. (for example, the subject, or verb are not stated.) For this reason, a Dependent Clause depends on another clause in order to become a complete statement
Ex.
Before going to class, Terry ate an apple.
In this example, the dependent clause, "Before going to class," did not make a complete statement, thus it relied on the Independent clause, "Terry went to class." In order to form a proper sentence.
The use of Dependent and Independent clauses can add to the depth of your writing, allowing you to add detail, as well as draining monotony from aa story.