Noun is a name of person, animal, thing that is, living or nonliving things. So the phrase which works as a noun is called as a Noun Phrase. That is, a group of words acts as a noun.
a. Studying early in the morning is the best.
In this, ‘studying early in the morning’ does not have a subject and predicate. So, it is a phrase and subject of the verb ‘is’. So it is a noun phrase.
If we ask question, what is the best? We get the answer ‘studying early in the morning’.
b. Chetan enjoys dancing on the stage.
‘dancing on the stage’ does not have subject and predicate. So it is a phrase. If we ask the question, “What does Chetan enjoy?” We get the answer, ‘dancing on the stage’. So ‘dancing on the stage’ is the object of the verb ‘enjoys’ and acts like a noun. So it is a noun phrase.