You will find the modern approach to this question, what is a phrase, in the page on English Phrases.
On this page, you have a traditional approach that is still valuable for teachers, parents and students.
It will help parents and teachers who have learned grammar in the old days and want to help their children, grandchildren or students to learn today's grammar.
This page and the page on English phrases read one after the other will help remove whatever confusion they have about this topic. In fact, the old knowledge can help them to understand the new in greater depth.
Today's students too can gain from this page for it can make them better informed about different approaches to the study of grammar. It can help sharpen their minds as well.
A phrase was defined as a group of words, which together did the work of a particular part of speech. So...
An adjective phrase was described as "a group of words which does the work of an adjective."
It is a pen of green colour.
In this sentence, the group of words of green colour describes the noun pen. The phrase is equivalent to the adjective green in the sentence: It is a green pen.
A noun phrase was described as "a group of words which does the work of a noun."
A group of words that acted in any of the following capacities was called a noun phrase.
See the sentence...
He has helped a few needy young men.
The group of words a few needy young men is a noun phrase because the group acts as the object of the verb has helped.
The traditional noun phrase and the modern noun phrase are not different...only, that we look at the same thing from two different viewpoints.
While in traditional grammar you looked at the function ("does the work of.."), in modern grammar you look at the structure (head word, modifiers, complement, etc) of the group of words.
In the case of a noun phrase, you get the same result, except that in traditional grammar, a single-word noun or pronoun would not be called a phrase.
An adverb phrase was described as "a group of words that does the work of an adverb."
Take the sentence...
She wrote it in the morning.
The group of words in the morning is an adverb phrase because it tells us something more about the verb wrote.
Q: wrote when?
A: in the morning.
Please note that when we look at structure (as in modern grammar) the words in the morning, are a prepositional phrase with the preposition 'in' as the head word.
Modern grammar does not avoid looking at functions of groups of words such as, in the morning. It considers these word groups as adverbial complements or adverbial adjuncts, depending upon whether they are essential to a sentence or not.