The Miracle of the Crimson Wool
These lengths of wool were specifically dyed crimson on account of the verse which reads, "Though your sins are as scarlet, they shall whiten as snow; though they be red like crimson, they shall be white as wool" (Isaiah 1:18). It is related that a great miracle occured concerning this crimson-colored wool: For in addition to the piece which was tied to the scapegoat, a similar length was tied to the entrance of the Sanctuary where all could behold it, high up like a banner. The sage Rabbi Yishmael taught (Yoma 6, 8) that when the scapegoat reached its destination in the desert, this wool miraculously turned white before the eyes of all Israel, in keeping with the words of the prophet - and thus providing a Heavenly sign that the sins of the people had been atoned for.
The two goats thus prepared, the High Priest will now leave them be and proceed with other aspects of this singular day's ceremonies. He will return to the sacrifice and the azazel only later, after the services of the bullock and the incense are completed. All the various components and aspects of the Yom Kippur service must be done according to a specific order.