A noun is a person, place, thing, animal, or concept. In this sense, 'play' is a thing or concept as it can refer to an activity or entertainment.
It is typically used in the context of a game, sport, or drama, but it can also refer to any form of recreation.
'I love watching plays at the theatre.'
'This play was written by William Shakespeare.'
The singular and plural of 'play' are both spelled the same, but the plural is typically used to refer to multiple performances of the same play, or multiple games of some type of sport.
a verb is an action word and in this sense 'play' means to engage in some type of activity or amusement as a pastime.
'We play football on the weekends.'
'The children were playing tag in the park.'
'Can you play the guitar?'
The verb form of 'play' does not require an object. For example, you can say 'Let's play' to mean 'Let's play a game.' It can also be used as an intransitive verb, in which case it is usually used in the continuous form. For example, 'He was playing the piano.'