This is the 7692nd most frequent Russian word.
западных
"Западных" means "western" (genitive or plural form).
Here, 'западных' is used in its genitive plural form modifying the noun 'стран' to describe 'western countries'
Многие западных стран поддерживают санкции.
Many western countries support sanctions.
'Западных' functions as a genitive plural adjective modifying 'обществ' to specify 'western societies'
Культура западных обществ имеет свои особенности.
The culture of western societies has its own characteristics.
In this sentence, 'западных' acts as a genitive plural adjective describing 'традиций', indicating 'western traditions'