What is a sentence fragment?

see below

A sentence fragment is a group of words that look like a sentence but lacks the following:

1. complete thought
2. a subject
3. an action/predicate

Examples:

1. They are. (They are what? We have no idea what it is about "they".)

2. Wishing you all the best. (Who is wishing all the best? There is no subject.)

3. A walking, talking doll. (What about the walking, talking doll? Is the doll doing anything? Note that "walking" and "talking" in this case are not but adjectives describing the doll.)

A dependent clause is also a sentence fragment because it cannot stand alone.

Ex:

But he was angry. (The conjunction "but" makes the clause dependent. A dependent clause cannot stand alone. It needs an independent clause to complete its thought.)