A phrase is the unit of the grammatical hierarchy that is at the level above the word level meaning that words are the constituents of phrases.
It is made up of a group, or potential group of words, that are linked in some way.
It has an obligatory head, which is the central word of the phrase, and one or more optional modifiers which describe or limit the head word in some way.
Depending on what is the head of that phrase, a phrase may function in a sentence as a noun phrase, a verb phrase, an adjective phrase, an adverb phrase, a preposition phrase, etc. ‘The new student from Hungary’ (NP); ‘so beautiful’ (AdjP); ‘quite happily’ (AdvP); ‘ate the cake’ (VP); ‘in the yard’ (PP), etc.
A phrase may not make sense on its own because it may lack a main verb and its subject, e.g., ‘is coming’, ‘the tall boy’, etc.
Consider sentence (1) below:
That young child plays the piano very well.
The first three words, i.e., ‘that young child’ make a phrase. The words ‘that’ and ‘young’ are modifiers that limit and describe the head noun ‘child’. The last two words “very well” are also a phrase; ‘well’ is the head with ‘very’ modifying it. The middle word ‘plays’ is also a phrase though it only has a head word with no modifiers.
Therefore, sentence (1) above (which consists of only one clause) is divided up into a number of phrases. The main/head word in each clause is italicized.