This is the 2716th most frequent Russian word.
восточный
Eastern.
Here, 'восточную' is used as an adjective modifying 'кухню', indicating the subject's liking for cuisine typical of Eastern regions.
Я люблю восточную кухню.
I love oriental cuisine.
The word 'восточный' is serving as an adjective to describe 'ветер', specifying the direction from which the wind originates.
Восточный ветер приносит тепло.
The eastern wind brings warmth.
In this case, 'в восточной' refers to the relative position within the country's geographic division, specifying its eastern segment.