This is the 2604th most frequent German word.
bayerischen
"Bayerischen" means "Bavarian" in English.
Here, 'bayerischen' is used as an adjective describing 'Spezialitäten', in the plural form and nominative case.
Ich genieße die bayerischen Spezialitäten.
I enjoy the Bavarian specialties.
In this sentence, 'bayerischen' is an adjective modifying 'Alpen', also in the plural form but in the genitive case as it is describing possession.
Die Landschaft der bayerischen Alpen ist atemberaubend.
The landscape of the Bavarian Alps is breathtaking.
'Bayerischen' functions as an adjective here for 'Wäldern', in plural and dative case, indicating the location.