"검은색인 공이 있습니까?"
Translation:Do you have a black ball?
X는 검은색이다 - literally 'X is a black colour', less literally 'X is of black color'
검은 - black, 색 - colour, 이다 - to be
검은색인 X - black X (literally X that is black)
To the point: 인 is a form of verb 이다 (to be something) that can be roughly translated to English as 'that is something'. For example: 아들인 남자 - a man who is (someone's) son. 고양이인 동물 - an animal that is a cat.
At least this is how I understand it.