What does Mark 14:36 mean?

Abba is Aramaic for "father." By calling God "Father," Jesus is acknowledging two major aspects of His relationship to God. First, God loves Jesus as a father and wants the best for Him. Second, Jesus owes God His submissive obedience as a son does his father.

Ephesians 1:4 says that God "…chose us in him before the foundation of the world, that we should be holy and blameless before him…" God certainly knew that Adam and Eve would sin in the garden, and He knew their descendants would be unable to choose to obey Him. When the Trinity made the world, They knew the Son would have to sacrifice His life for Their creation.

In order to be a substitute for humans, the Son had to become human. That is, He had to take on human nature in addition to His God nature. This human side knows what the God side has planned. He knows that the suffering will be horrible, but short-lived. And He knows that the suffering will result in God glorified and humanity saved.

Jesus' human side also has its own will. If He had a choice, He would prefer not to go through the crucifixion. Even more so, however, Jesus is dreading the "cup." In the culture, one's "cup" was one's lot in life, whether good or bad. When Jesus gives the cup to the disciples at the Lord's Supper, they are taking on the life His blood provides, both the persecution that comes to His followers (Mark 10:38–39) and everlasting life in paradise (Mark 14:23–24).

The Bible also uses the concept of "the cup" as a spiritual metaphor for God's wrath. Revelation 14:10 describes the fate of those who take on the mark of the beast: "he also will drink the wine of God's wrath, poured full strength into the cup of his anger…" This is the "cup" that Jesus takes on the cross for believers. It's only logical that He would want to avoid it, but He finishes His prayer submitting to the wishes of His Father.