A Phrase is a group of words forming a part of a sentence without a subject and a finite verb. A phrase functions in the sentences mostly as a Noun, Adjective, Adverb or Verb and accordingly it is called a Noun Phrase, Adjective Phrase, Adverb Phrase or Verb Phrase (Phrasal Verb).
The Phrase that functions as a Noun in the sentence is called a Noun Phrase.
Let us look at the sentences.
An old man is calling me.
In this sentence, the phrase 'an old man' is functioning as subject of the verb 'is calling' and is, therefore, functioning as Noun; this is a Noun Phrase and it has been formed by the noun 'man' and the adjective 'old'.
Let us look at the sentences:
Waiting passengers became impatient.
In this sentence, the phrase 'waiting passengers' is functioning as the subject of the verb 'became' and is, therefore, functioning as a Noun; this is a Noun Phrase and is formed by the noun 'passengers' and the participle 'waiting'.
Let us look at the following sentences:
I want to complete the assignment.
In this sentence, the phrase 'to complete the assignment' is functioning as the object of the verb 'want' and is, therefore, functioning as Noun. This is Noun Phrase which has been formed together with the infinitive 'to complete' and its object 'the assignment'.
Let us look at the sentence:
John wants to be a minister.
In this sentence, the phrase 'to be a minister' is functioning as object of the verb 'wants' and is, therefore, functioning as Noun. This is a Noun phrase, formed together with the infinitive 'to be' and its complement 'a minister'.
Let us look at the sentence:
My mother wanted to walk slowly.
In this sentence, the phrase 'to walk slowly' is functioning as the object of the verb 'anted' and is, therefore, functioning as Noun. This is a Noun Phrase, which has been formed together with the infinitive 'to walk' and the adverb 'slowly' (modifying the infinitive 'to walk').
Let us look at the sentence:
He spends a lot of time in reading books.
In this sentence, the phrase 'reading books' is functioning as object of the preposition 'in' and is therefore functioning as a Noun. This is a Noun Phrase which has been formed by the Gerund 'reading' with its object 'book.
Look at the sentence:
People realize the importance of being honest.
In this sentence, the phrase 'being honest' is functioning as the object of the preposition 'of' and is therefore, functioning as Noun. This phrase is a Noun Phrase, which has been formed by the Gerund 'being' and its complement 'being'.
Let us look at the sentence:
He enjoys running fast.
In this sentence, the phrase 'running fast' is functioning as object of the verb 'enjoys' and is, therefore, functioning as Noun. This is a Noun Phrase, formed by the Gerund 'running' and the adverb 'fast' (modifying the Gerund 'running').
Also See: Function of Noun Phrase , Adjective Phrase , Adverb Phrase