This is the 11857th most frequent Russian word.
западную
"Западную" translates to "western" (feminine singular accusative form) in English.
In this sentence, 'западную' is in the accusative case, feminine singular form, describing the feminine noun 'часть' (part).
Мы отправляемся в западную часть города.
We are going to the western part of the city.
Here, 'западная' is in the nominative case, feminine singular form, modifying the feminine noun 'граница' (border).
На этой карте изображена западная граница страны.
On this map, the western border of the country is depicted.
'Западного' in this example indicates the genitive singular form of 'западный' and relates to 'региона' (region), showing possession or origin.