Sentence fragments are a common mistake. A sentence fragment is an incomplete sentence. It could be a prepositional phrase. Or it could be a dependent clause.
An English sentence must have a subject and a verb of its own. Study the sentences given below.
Mike took out his pen.
He started writing.
As you can see, both sentences given above have a subject and a verb of their own. They also make complete sense.
A sentence can have any number of clauses but it must have at least one main or independent clause.
A dependent or subordinate clause, too, will have a subject and a verb of its own. However, a dependent clause cannot stand on its own. It needs to be attached to an independent clause.