This is the 5975th most frequent Russian word.
серой
"Серой" means "gray" (color) in English.
In this sentence, 'серой' is the instrumental case of the adjective 'серый,' agreeing with 'шарф' (scarf) to describe its color.
Она носит серой шарф.
She is wearing a grey scarf.
Here, 'серой' is used in the prepositional case to agree with 'улице' (street), indicating the color when referring to a location.
Мы гуляли по серой улице.
We walked along the grey street.
'Серой' in this context is in the prepositional case, modifying 'обложке' (cover), describing the attribute of the cover's color.