Answer: The gospels contain an account of the time the disciples and Jesus spent in the Garden of Gethsemane, just before Jesus was arrested. In the garden Jesus prayed to his Father three times, saying, “My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will”—the KJV says, “Let this cup pass from me” (Matthew 26:39). A little later, Jesus prays, “My Father, if it is not possible for this cup to be taken away unless I drink it, may your will be done” (Matthew 26:42). These prayers reveal Jesus’ mindset just before the crucifixion and His total submission to the will of God.
The “cup” to which Jesus refers is the suffering He was about to endure. It’s as if Jesus were being handed a cup full of bitterness with the expectation that He drink all of it. Jesus had used the same metaphor in Matthew 20:22 when prophesying of the future suffering of James and John. When Jesus petitions the Father, “Let this cup pass from me,” He expresses the natural human desire to avoid pain and suffering.
Jesus is fully God, but He is also fully human. His human nature, though perfect, still struggled with the need to accept the torture and shame that awaited Him; His flesh recoiled from the cross. In the same context, Jesus says to His disciples, “The spirit is willing, but the flesh is weak” (Mathew 26:41). In praying, “Let this cup pass from me,” Jesus was battling the flesh and its desire for self-preservation and comfort. The struggle was intense: Jesus was “overwhelmed with sorrow to the point of death” (Matthew 26:38), and Luke the physician observed that Jesus was sweating blood—a sign of extreme anguish (Luke 22:44). If anything shows that Jesus was indeed fully man, this prayer is it.
Jesus knew of what was to come (see Mark 8:31). The agony He faced was going to be more than physical; it would be spiritual and emotional, as well. Jesus knew that God’s will was to crush Him, to allow Him to be “pierced for our transgressions” and wounded for our healing (Isaiah 53:5–10). Jesus loves mankind, but His humanity dreaded the pain and sorrow He faced, and it drove Him to ask His Father, “Let this cup pass from me.”
Jesus’ prayer to “let this cup pass from me” contains two important qualifications. First, He prays, “If it is possible.” If there was any other way to redeem mankind, Jesus asks to take that other way. The events following His prayer show that there was no other way; Jesus Christ is the only possible sacrifice to redeem the world (John 1:29; Acts 4:12; Hebrews 10:14; Revelation 5:9). Second, Jesus prays, “Yet not as I will, but as you will.” Jesus was committed to the will of God, body, mind, and soul. The prayer of the righteous is always dependent on the will of God (see Matthew 6:10).
In Gethsemane, Jesus conquered the flesh and kept it in subjection to the spirit. He did this through earnest prayer and intense, willful submission to God’s plan. It is good to know that, when we face trials, Jesus knows what it’s like to want God’s will and yet not to want it; to act out of love yet dread the hurt that often results; to desire righteousness and obedience, even when the flesh is screaming out against it. This conflict is not sinful; it is human. Our Savior was “fully human in every way, in order that he might become a merciful and faithful high priest in service to God” (Hebrews 2:17). He had come “to seek and to save the lost” (Luke 19:10), and He accomplished His mission, even though it meant drinking the cup of suffering to the bitter end.
http://www.gotquestions.org/let-this-cup-pass-from-me.html