Definitions

An independent clause is a group of words that can stand on their own as a sentence. Something like "Johnny ate the apples." An independent clause has to have the same requirements as a sentence (Subject and verb), and has to be able to stand alone.

The reason it isn't the same thing as a sentence is that we discuss independent and dependent clauses as parts of simple, compound, and complex sentences. Therefore, the sentence could be "Johnny ate the apples, which prevented mom from making her famous apple pie." "Johnny ate the apples" is still an independent clause, but it is part of a larger sentence (in this case it is joined to a dependent clause and the sentence is a complex sentence).

If the sentence were joined to another independent clause, the sentence would be compound (and yes, you can have compound-complex sentences, which require at least two independent clauses and one dependent clause).
An independent clause is a clause that can stand alone by itself. It is basically a simple sentence, For example : "I went to the movies." it is a simple sentence.

Example 2: "I went to the movies, because I did not want to stay at home."

"I went to the movies" is an independent clause, because it can stand alone and at the same time make sense. While "because I did not want to stay at home." is a dependent clause because it does not make sense when it is alone.