Black Jack (ブラック・ジャック), whose real name is Hazama Kuro (間 黒男), used to live near a military site when he was young, which was filled with unexploded ordinance. One day he and his mother unwittingly stepped on and detonated a hidden mine. His mother went into a coma and eventually passed away. Black Jack almost died too but after many surgeries by Dr Honma Jotaro eventually managed to recover. Part of the reconstruction of his body was skin grafting onto the left side of his face. It was donated by his half-African friend Takashi, hence why it is darker than his natural skin color. He refused to have the skin colors match or the scars removed out of respect for Takashi. Incidentally, his white hair is also a side-effect of the explosion (due to the shock).
For more information read the Black Jack manga Volume 2, Chapter 7; Volume 7, Chapter 5; Volume 11, Chapter 1; and Volume 12, Chapter 7.