Why many Catholics believe that Mary is co-redemptrix? Where does the belief come from? Why is her intercession believed to be necessary? Please provide Biblical evidence for the belief as well as Traditional sources.
Mary is co-redemptrix just means she has cooperated with Jesus Christ for our salvation. Explanations can be found in Lumen gentium quoted below :


  
  There is but one Mediator as we know from the words of the apostle, "for there is one God and one mediator of God and men, the man Christ Jesus, who gave himself a redemption for all" (1Tm 2,5-6). The maternal duty of Mary toward men in no wise obscures or diminishes this unique mediation of Christ, but rather shows His power.
  Thus Mary, a daughter of Adam, consenting to the divine Word, became the mother of Jesus, the one and only Mediator. Embracing God's salvific will with a full heart and impeded by no sin, she devoted herself totally as a handmaid of the Lord to the person and work of her Son, under Him and with Him, by the grace of almighty God, serving the mystery of redemption. Rightly therefore the holy Fathers see her as used by God not merely in a passive way, but as freely cooperating in the work of human salvation through faith and obedience.
  This union of the Mother with the Son in the work of salvation is made manifest from the time of Christ's virginal conception up to His death it is shown first of all when Mary, arising in haste to go to visit Elizabeth, is greeted by her as blessed because of her belief in the promise of salvation and the precursor leaped with joy in the womb of his mother (cf. Lc 1,41-45). This union is manifest also at the birth of Our Lord, who did not diminish His mother's virginal integrity but sanctified it, (Cf Eph. 1:18) when the Mother of God joyfully showed her firstborn Son to the shepherds and Magi. When she presented Him to the Lord in the temple, making the offering of the poor, she heard Simeon foretelling at the same time that her Son would be a sign of contradiction and that a sword would pierce the mother's soul, that out of many hearts thoughts might be revealed (cf. Lc 2,34-35). When the Child Jesus was lost and they had sought Him sorrowing, His parents found Him in the temple, taken up with the things that were His Father's business; and they did not understand the word of their Son. His Mother indeed kept these things to be pondered over in her heart (cf. Lc 2,41-51).
  In the public life of Jesus, Mary makes significant appearances. This is so even at the very beginning, when at the marriage feast of Cana, moved with pity, she brought about by her intercession the beginning of miracles of Jesus the Messiah (cf. Jn 2,1-11). In the course of her Son's preaching she received the words whereby in extolling a kingdom beyond the calculations and bonds of flesh and blood, He declared blessed (cf. Mc 3,35 par. and Lc 11,27-28) those who heard and kept the word of God, as she was faithfully doing (cf. Lc 2,19 2,51). After this manner the Blessed Virgin advanced in her pilgrimage of faith, and faithfully persevered in her union with her Son unto the cross, where she stood, in keeping with the divine plan, (Cf. Jn. 19:25) grieving exceedingly with her only begotten Son, uniting herself with a maternal heart with His sacrifice, and lovingly consenting to the immolation of this Victim which she herself had brought forth. Finally, she was given by the same Christ Jesus dying on the cross as a mother to His disciple with these words: "Woman, behold thy son" (cf. Jn 19,26-27).