An independent clause is a clause that has both subject and verb and conveys a complete thought. It can also be a standalone sentence by itself.
E.G. "Jim bought a new car."
A dependent clause has a subject and a verb but is not a complete thought. Dependent clauses typically contain a 'dependent-making-word' (after although, because, before, even, etc.) at the beginning of the clause.
E.G. "If I go to the store"
*This sentence is not a complete thought and would be combined with an independent clause
E.G. "If I go to the store I'll buy some bread."
I agree with Tom's explanation. I will add that dependent clauses are also called subordiante clauses, and again, it is important to keep in mind that the sentence/idea is incomplete if it has only a subordiante clause.
Sometimes, a sentence consists of more than one clause, but it does not automatically mean that one of them is subordiante because there ay also be coordiante clauses. These are clause which can exist and make a sentence dependently.
e.g. I am hungry, have a headache, and I want to go home; unfortunately, I can't.
A dependent clause creates a question in the mind of the reader that needs to be answered. If you read a sentence you have written and you have a question still unanswered, you need to "fulfill" your dependent clause. I often say that the dependent catchword (Because, even, if, although, etc.) must be "fulfilled" or answered.