sentence fragment

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A phrase or clause that is punctuated and capitalized as a sentence but does not constitute a complete grammatical sentence.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun an incomplete sentence; a phrase or clause that is punctuated and capitalized as a sentence but does not constitute a complete grammatical sentence. It is usually caused by the failure to include a subject and a verb in a sentence or as the result of beginning a sentence with a subordinate conjunction or relative pronoun.