“let this cup pass from me.” This use of “cup” is an idiom based on the custom of the drink at a meal being passed around from one person to another. There was usually only one cup, so people got what was in the cup without having a choice. Thus the cup at a meal was very similar to life: we often do not have a choice of what happens to us, we get the “cup” that we get. In this verse, Jesus is asking God if he can avoid partaking of the “cup” that is being passed to him.
[For more on the custom of the cup, see commentary on Psalm 11:6.]