What is the difference between a complete sentence and a sentence fragment?
A complete sentence is a set of words containing a subject, a verb, and a complete thought; a sentence fragment is missing one or more of those three essential elements.
Here is an example of a complete sentence: They wrap gifts.
They is the subject (or who the sentence is about), wrap is the verb (or a word that denotes an action), and gifts completes the thought because it is the object of the verb wrap. Without the object of wrap, we would not know what is wrapped.
They wrap is a sentence fragment (also often called an "incomplete sentence") because it is missing a word that would complete the thought that begins with They wrap. Notice that They wrap contains two out of three of the elements that are needed to make a sentence complete: the subject They and the verb wrap. The sentence is a fragment because it is missing a complete thought, which is one of the three elements that make up a complete sentence.