Sentence fragments

A sentence fragment is a word, a phrase, or a dependent clause used (and punctuated) as a sentence.

(PREPOSITIONAL) PHRASE*
during lunch (PHRASE)
During lunch. (PHRASE PUNCTUATED AS SENTENCE)

I’m going to call her during lunch. (CORRECT)
I’m going to call her. During lunch. (INCORRECT)

DEPENDENT CLAUSE:
when the sun comes up (DEPENDENT CLAUSE)
When the sun comes up. (DEPENDENT CLAUSE PUNCTUATED AS SENTENCE)

The rooster crows when the sun comes up. (CORRECT)
When the sun comes up, the rooster crows. (CORRECT)
The rooster crows. When the sun comes up. (INCORRECT)

A dependent clause cannot stand alone as a complete sentence.

AND SEE: Sentence fragments: pro and con

*NOTE: There are several different kinds of phrases.

Adjective, adjective phrase, adjective clause

SEE ALSO: Phrase versus clause

An adjective “modifies” (“adds information to”) a noun. Adjective phrases and adjective clauses also modify nouns.

adjective
black cat
Black” is the adjective.

adjective phrase
the cat in the hat
In the hat” is an adjective phrase.
(remember: A phrase does not have a subject-predicate structure.)

adjective clause (also called “relative clause“)
the cat who lives in the house
Who lives in the house” is an adjective clause.
(remember: A clause has a subject and a predicate. And: a clause can be independent or dependent. A sentence has at least one independent clause.)

structure of the adjective clause:
who || lives in the house
who [SUBJECT] || lives [VERB] in the house [PREDICATE]
“Who” is the SUBJECT.
“Lives” is the VERB.
“Lives in the house” is the COMPLETE PREDICATE.
NOTE: An adjective clause is a dependent clause. It cannot stand alone as a complete sentence.

REVIEW
Who” is a pronoun. It stands in for (or refers to) “cat.” Pronouns take the place of nouns or noun phrases.

fyi:
Technically, you’re not supposed to use “who” to refer to animals. “Who” refers to people; “that” or “which” refers to animals.

I break this rule intentionally, but I want you to know that the rule exists.

Phrase versus clause

This is a phrase:
in the hat
This is not a phrase:
hat the in

This is a phrase (not a clause):
Rex the dog
This is a clause:
Rex barked

The easiest type of clause to identify has a stated subject and a predicate:
Rex [SUBJECT] || barked [PREDICATE].
Rex [SUBJECT] || barked at the cat [PREDICATE].
(“Barked” is the verb. “Barked at the cat” is the complete predicate. The predicate includes the verb.)
Rex the dog [SUBJECT] || barked at the cat [PREDICATE].
(“Rex the dog” is the complete subject. “Barked at the cat” is the complete predicate.)

A phrase does not have the subject-predicate structure of a clause: 
on the boat
in the classroom
would have been
stand up

NoteIn everyday language the term “phrase” refers to two or more “grammatically related” words. (“the big dog” not “dog big the”) Grammarians, however, also use the word “phrase” to apply to just one word because a single word can serve the same function as a phrase:

Sentence Verb phrase
Rex is barking. is barking
Rex barked. barked
   
Sentence Noun phrase
Rex barked. Rex
Rex the neighbor dog barked. Rex the neighbor dog