This is the 392nd most frequent Ukrainian word.
українським
"Ukrainian" (adjective, instrumental case).
In this sentence, 'українським' is an adjective in the instrumental case, describing 'народом' (the people), expressing pride or a related feeling.
Я пишаюся українським народом.
I am proud of the Ukrainian people.
Here, 'українським' functions as an adjective in the instrumental case, describing 'містечком' (a small town), indicating the characteristic of the town being Ukrainian.
Ми зараз подорожуємо українським містечком.
We are currently traveling through a Ukrainian town.
'Українським' in this sentence is an adjective in the instrumental case that describes 'режисером' (director), identifying the director's nationality.