They went to a place called Gethsemane, and Jesus said to his disciples, “Sit here while I pray.”  He took Peter, James and John along with him, and he began to be deeply distressed and troubled. “My soul is overwhelmed with sorrow to the point of death,” he said to them. “Stay here and keep watch.”

Going a little farther, he fell to the ground and prayed that if possible the hour might pass from him. “Abba, Father,” he said, “everything is possible for you. Take this cup from me. Yet not what I will, but what you will.”

Then he returned to his disciples and found them sleeping. “Simon,” he said to Peter, “are you asleep? Couldn’t you keep watch for one hour? Watch and pray so that you will not fall into temptation. The spirit is willing, but the flesh is weak.”
- Mark 14:32-38

There are two cups in Mark 14: the cup that all the disciples drink from—the cup of the new covenant—and the cup that Jesus will drink from. The latter is an Old Testament image representing God's judgment:

"Awake, awake! Rise up, Jerusalem, you who have drunk from the hand of the LORD the cup of his wrath, you who have drained to its dregs the goblet that makes people stagger." (Isaiah 51:17)

The idea of judgment as a cup to be drunk originates from the rebellion of Israel at the foot of Mount Sinai. While Moses is on the mountain receiving the Ten Commandments—which begin with the commands not to worship other gods or make idols—the people below are doing exactly that: making an idol and worshipping it. In response, Moses grinds up the idol, sprinkles the powder into the water, and makes them drink it. Symbolically, they are forced to consume the consequences of their idolatry.

Will we experience the consequences of our sin? No. At the heart of the Christian faith is the belief that Jesus takes upon himself the consequences of human rebellion. He drinks the cup of wrath so that those who trust in him do not have to. Instead, we are given the cup of grace—a gift that combines not receiving what we deserve (judgment) with receiving what we do not deserve (eternal life in the love of God).