This is the 7213th most frequent Russian word.
верхней
"Upper" or "top" (adjective, feminine genitive or dative case).
The word 'верхнюю' is the accusative feminine singular of 'верхний', indicating the 'upper' shelf among others.
Я положил книгу на верхнюю полку.
I placed the book on the upper shelf.
Here, 'верхнем' is the prepositional masculine singular form of 'верхний', specifying the 'top floor'.
На верхнем этаже находится библиотека.
On the top floor, there is a library.
In this sentence, 'верхнего' is the genitive masculine singular form of 'верхний', describing the 'upper corner' in relation to the room's geometry.