they are a group of words that look like sentences, but aren't. every sentence must have an independent and dependent clause to be an accepted sentence. an independent clause can stand on its own, hence the name, but a dependent clause can, hence the name. it is dependent on the independent clause.
for example:
when we got in the car.
(this is a dependent clause. what happened when you guys got in the car? this is a fragment. it does not form a complete thought.)
we rolled down the windows.
(this is an independent clause. although we don't know why you rolled down the windows or what windows you are rolling down, this is an accepted as a full sentence.)
when we got in the car, we rolled down the windows.
(as you can see, in this sentence we have connected the two clauses. the sentence makes much more sense )