An independent clause must have a subject and a verb; it can stand alone as a complete sentence.
There are four major types of sentences, or independent clauses.
I. Simple Sentence (s+v):  The boy hit the ball.
II. Compound Sentence (s+v,and s+v):  The boy hit the ball, and the third baseman caught it.
III. Complex Sentence (s+v+DC[s+v]):  The boy, who wanted desperately to make the team, struck out.
IV. Compound/Complex (s+v,and s+v+DC[s+v]): The boy, who wanted desperately to make the team, struck out, but he hit a homerun later in the game.
Independent Clauses