This is the 2002nd most frequent Russian word.
украинское
"Украинское" means "Ukrainian" (adjective, relating to Ukraine).
Here, 'украинское' serves as an adjective modifying 'Солнце', describing it as associated with Ukraine.
Украинское Солнце светит ярко.
The Ukrainian Sun shines brightly.
In this example, 'украинское' is an adjective describing 'блюдо', specifying it as a dish from Ukrainian cuisine.
Мне понравилось украинское блюдо, борщ.
I liked the Ukrainian dish, borscht.
Here, 'украинское' is used as an adjective qualifying 'кино', indicating that the cinema is related to Ukraine, either by production or theme.