This is the 5979th most frequent Polish word.
śląskiej
"Śląskiej" means "Silesian" (relating to Silesia, a historical region in Europe).
In this sentence, 'śląskiej' is used as an adjective describing 'tradition,' specifically referring to the traditions of Silesia.
Kuchnia śląskiej tradycji jest bardzo smaczna.
The cuisine of Silesian tradition is very tasty.
Here, 'śląskiej' is an adjective modifying 'village,' indicating that the village is located in or related to Silesia.
Mieszkańcy śląskiej wioski przygotowali festiwal.
The inhabitants of the Silesian village organized a festival.
In this case, 'śląskiej' is an adjective describing 'culture,' referring to the cultural aspects associated with Silesia.