Sentence fragments are incomplete sentences. Fragments occur in several ways. Usually a fragment is a dependent clause that begins with a subordinate conjunction and requires an independent clause to complete a complex sentence. Several examples follow.
The Olympics take place in Greece. (Simple Sentence)
When the Olympics take place in Greece, security will be extremely tight. (Complex Sentence includes both a dependent and an independent clause).
Another type of fragment is one that eliminates either the subject or the verb or both in the sentence.
The boys in the band were on the bus. (Missing verb "were")
The boys in the band on the bus are traveling to Atlanta for a concert. (Missing verb "are traveling")
He looked surprised when he first caught sight of her.
When he first caught sight of her, he stopped in his tracks to admire her.