This is the 4973rd most frequent Russian word.
красного
"Красного" means "red" (genitive or accusative singular, masculine or neuter, or genitive singular feminine in some contexts).
The word 'красного' is in genitive case denoting the color attribute of the dress.
Я купил платье красного цвета.
I bought a dress of red color.
Here, 'красного' connects with 'цвета' (color) to describe possession and attribute.
У моего друга машина красного цвета.
My friend has a car of red color.
'Красного' describes 'оттенка' and is in the genitive case to specify the shade.