Many icons show Saint Nicholas with Jesus on one side and Mary the Blessed Mother on the other. They hold symbols of a bishop's office: the Book of the Gospels and an omophorion. They appeared this way in two events of Nicholas' life. The first was when he was selected to be consecrated as a bishop. The second was at the Council of Nicaea. They symbolize God's favor resting upon Nicholas and confirm his vocation as a bishop.
After Nicholas, who had been foretold in a vision to one of the bishops charged with selecting the new bishop for the See of Myra, came to the church and was recognized as the one in the vision, he modestly refused to accept the office. The other bishops persisted and led him to the throne, despite his resistance. Nicholas was compelled to accept the office, as he recalled the vision that had come to him in the days before Bishop John's death. In the vision Nicholas saw before him Jesus the Savior in all his glory, giving him a Book of the Gospels covered with gold and pearls. On the other side of himself he saw the Theotokos who placed a bishop's omophorion on his shoulders. And so Nicholas came to believe it was truly God's will for him to serve as a bishop.
At the Council of Nicaea, after Nicholas had become so enraged at Arius for promoting false teachings that he hit him in the face, Nicholas was stripped of his office and put in jail. While there, Jesus and Mary, his Mother, appeared in a vision * to Constantine and all the bishops of the Council, in which Jesus and Mary gave the objects that identify a bishop—the Book of the Gospels and an omophorion—to Nicholas. This convinced the Council to reinstate Nicholas to the office of bishop.
* In other versions of the story 1) Jesus and Mary with Nicholas appear in a dream to Constantine who then decrees that Nicholas be reinstated, or 2) Jesus and Mary visit Nicholas, who is praying in his cell, and in the morning the jailer finds him praying with the Gospel Book, wearing an omophorion. This is reported to the Council which then reinstates Nicholas.
SOURCE for the vision at the time of Nicholas' consecration: Service, Akathist, Life and Miracles of Saint Nicholas the Wonderworker, Holy Trinity Monastery, Jordanville, New York. A complete translation of the Life and the Miracles of St. Nicholas as it appears in The Lives of the Saints in the Russian Language as set forth according to the guidance of the Menologiion of St. Dimitry of Rostov, Moscow, Synodal Press, 1903.