A sentence with no subject or verb is an incomplete sentence. That would be a sentence fragment.
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A complete sentence requires a subject and that subject'spredicate, excluding any subject/predicate pairs that are part of a dependent clause.
Sentence fragments often appear as short answers to questions, where the subject or predicate is already known. This is acceptable in speech but considered incorrect writing.
Ex Q: "What are you doing?"
Ex A: "Running home."
The answer is a sentence fragment because it has no subject ("home" is an object; it's not what's doing the running).
Ex Q: "What are your hobbies?"
Ex A: "Hiking, boating, and watching people climb trees."
The answer is a sentence fragment because it has no subject. Notice that it contains a complete subject-predicate pair ("people climb"), but that pair is part of an object clause.
Ex Q: "Who keeps poking me in the back?"
Ex A: "Stefan, with that pencil he just sharpened."
The answer is a sentence fragment because it has no predicate. Again, there is a subject-predicate pair ("he sharpened") but that pair is part of a dependent clause.
Special case: Imperative
Many languages allow the omission of a subject because the verb conjugation implies only one (or very few) matching pronouns. In English, that's not usually the case, except with commands. When you write a command, the subject "you" can be left out:
Ex: "Stop goofing off!"
The implied subject is 'you' and the predicate is 'stop'. This is a valid sentence.
Do you work? is a complete sentence; it is not a sentence fragment.
"She wave." is fragment but "She waves" is a sentence.
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Make each fragment into a complete sentence.
"After the storm," is not a complete sentence so it is a fragment.
A sentence is a fragment when you do not have a noun/pronoun and a verb.
A fragment sentence is a partial sentence. It does not have everything it needs to be a full sentence. For example: "The dog" is a fragment.
In order to not write a sentence fragment, you must always have a subject in your sentence and a predicate. For example: Fragment: Went to the movies. Sentence: I went to the movies.