This is the 12673rd most frequent Russian word.
коричневым
"Коричневым" means "brown" (instrumental case, singular masculine form).
In this sentence, "коричневым" is used as an instrumental case of the adjective "коричневый" agreeing with "цветом," describing the color something is painted in.
Этот кирпич окрашен коричневым цветом.
This brick is painted in brown color.
Here, "коричневым" serves as an instrumental case, describing the color of the ball formed by the curled-up cat.
Кошка свернулась коричневым клубком.
The cat curled up into a brown ball.
In this context, "коричневым" is used as an instrumental case to describe the color of the textiles used for decoration.