A complete sentence contains a subject and a predicate. First, let me clarify some of these terms. A subject is the main noun or pronoun that the sentence is about. The predicate contains the main verb that either demonstrates the subject's action or is linking the subject to another noun or adjective in the predicate (as in a linking verb). Not only does the predicate contain the verb, but it also contains complements, which are any words that modify or accompany the verb. In order for a sentence to be complete, it must have at least one subject and one predicate. Another word for a complete sentence is an independent clause.
The opposite of a complete sentence would be an incomplete sentence, or a fragment. Usually, a fragment is missing one of these necessary components (a subject or a verb) and is not an independent or complete thought. It generally doesn't make any sense. In addition, another opponent to the complete sentence is the run-on sentence. Unlike the fragment, the run-on contains both a subject and a verb; however, it usually consists of multiple sentences crammed together. It goes on and on and on without proper punctuation or conjunctions to help join ideas.