Identifying a subordinate clause in a sentence

A subordinate clause is a part of the sentence that cannot stand on it's own. An independent clause will have a subject and a verb, a subordinate (also called dependent) clause will usually lack either one so that it's not a complete thought on its own.
 
Here's an example: The cat jumped off of the table then quietly purred. 

"The cat jumped off of the table" is an independent clause because it's still a complete thought on its own. However, "then quietly purred," is a subordinate or dependent clause because it is just not a full sentence and won't make sense alone.