A cup is a common reference in the Old Testament to the wrath of God against sin - cp. Isaiah 51:17, 22. The next day, Jesus would bear the entire scope of the wrath of God against sin that otherwise would have been born by every sinner.The fullness of God's wrath for our sin would fall against Him - cp. Isaiah 53:10. Part of that wrath would necessitate the forsaking of the Son by the Father as Jesus became sin for us - 2 Corinthians 5:21. The prayer concerning this cup was an indication of how the humanity of our Savior dreaded the events of the morning. However, it is a perfect example of how surrendered He was in every way - cp. John 5:30. Consequently, instead of showing a hesitation to provide the atonement, it demonstrated the resolve to fulfill the plan of God for the redemption of man.
There is another view - somewhat obscure - that teaching a completely different point of view. This is less likely, but is worth mentioning. As Jesus was communing with the Father, he was being assaulted by the enemy (Satan) in an effort to thwart the events of Calvary. The intensity of this Satanic assault became so severe that Jesus physical well-being was threatened - cp. Matthew 26:38; Luke 22:44. As He was physically imperilled, He knew that Satan would love nothing more than to kill Him on the spot and thereby eliminate the possibility of the work of the cross. Realizing the intensity of Satan's attempts, prays that God would protect Him by delivering Him through the attempt of Satan to kill Him - that this was the cup Jesus was expressing a desire to avoid. Nevertheless, Christ was willing to endure whatever God willed for Him.
I trust these views provide some insights that God's Spirit can use to bring this passage into focus for you.