This is a poignant scene as it is the last recorded interaction that Jesus had before He enters Jerusalem. The interaction, in my opinion, serves as a launching point for Jesus' actions in Jerusalem. We learn that Jesus and His disciples were in Jericho and were leaving for Jerusalem (about a 16 mile walk - quite a ways away). As they were leaving, two blind men yell at Jesus. They refer to Him as "Lord, son of David." This designation has special significance. These men recognized Jesus as the Messiah in the line of David; as promised in the Hebrew Bible. There must have been rumors or first hand accounts of Jesus' healing and other miraculous works. This would account for their insistence that Jesus turn his attention to them and and Him to "have mercy on us!" Regardless of the pressure from the crowd to stop, they continued their plea for help.
Jesus asks a confounding question, "What do you want me to do for you?" It seems to be obvious what the men want: they are blind and want their sight. Like Jesus speaking in parables, I believe the question here is one that is not straightforward. It's about more than physical healing; or to be more clear, Jesus knows that it is about more than physical healing. Verse 34 reveals what it is really all about: following Jesus. The healing that Jesus does is about more than just regaining sight. It's about what happens because of the healing. These men gain a new purpose, a new passion, a new life. As a result of their healing they start following Jesus. Theses men recognize Jesus for who He is. Consequently, their healing ends up being about more than their sight. They got a lot more than they bargained for!
In terms of the Kingdom, these healings (along with the others in the Gospels) are signs that the Kingdom of God has been inaugurated. The old is being made new. What has gone wrong is now being made right. The broken is now being made whole. They give us a whole lot more than we bargained for.