White is the color of the cassock worn by the Holy Father. This custom dates from the pontificate of Pope St. Pius V (1566-72), who was a Dominican priest and wanted to retain the color of his white religious habit.
Cardinals wear red as a sign of the blood of the martyrs: Pope Blessed John Paul II stated at an investiture of cardinals in 1998: “Red is a sign of the dignity of the office of a cardinal, signifying that you are ready to act with fortitude, even to the point of spilling your blood for the increase of the Christian faith.”