This is the 1234th most frequent Russian word.
народного
"Narodnogo" means "of the people" or "popular" in English.
In this sentence, 'народного' modifies 'искусства' to mean 'folk art', indicating the nature or category of the artwork.
В этом году открывается новый народного искусства музей.
This year, a new museum of folk art is opening.
Here, 'народного' describes 'творчества', referring to creativity originating from the people or traditional folklore.
Наш театр представляет спектакль из народного творчества.
Our theater presents a play from folk creativity.
In this context, 'народного' relates to 'движения', denoting a movement that is of or for the populace.