What are Fragments in a paragraph?

A sentence fragment has no object; either no subject or no verb. As has been pointed out on The Simpsons, "Sentence Fragment" is, itself, a sentence fragment. For example, "The fox, the dog." Doesn't have a verb - it doesn't stand up as a sentence. "The fox jumps the dog." Becomes a sentence with the addition of the verb. Another example, "Looking into the distance, saw the house." Is a sentence fragment as it has no subject, adding a subject makes the sentence: "Looking into the distance, he saw the house."