This is the 11235th most frequent Russian word.
датские
"Датские" means "Danish" in English.
In this sentence, 'датские' is an adjective modifying the noun 'печенья', describing their origin (Danish).
Я купила датские печенья в магазине.
I bought Danish cookies in the store.
Here, 'датские' is used as an adjective to designate the national cuisine associated with Denmark.
Друзья пригласили меня попробовать датские блюда у них дома.
Friends invited me to try Danish dishes at their home.
In this example, 'датском' (a form of 'датские') describes the style of decoration, indicating its cultural inspiration.