A sentence fragment is a separate sentence within the context of a statement or narrative constructed as a qualifier. Common in modern usage, it's considered incomplete grammar by some literary authorities. Defenders of the use of fragments contend that fragments are a natural part of usage, often idiomatic references, and that their grammatical context is as natural associative statements. Strictly speaking, fragments are basically severed parts of sentences. They should theoretically have conjugations or qualifiers, but often they're self explanatory, and the use of those additional properties is turgid or redundant.
Examples of Sentence Fragment:http://owl.english.purdue.edu/owl/resource/620/01/