The kingdom of heaven is like yeast that leavens a batch of wheat flour until the whole batch was leavened. Jesus' likening of the kingdom of heaven to the ACTION of yeast definitely brought a new twist to his audience's understanding of the kingdom. While this is not to say that our present understanding of the kingdom proclaimed by Jesus is any better, however, Jesus introduced to those listening to him a totally new perspective of the kingdom.
To the immediate recipients of Jesus' teaching, the kingdom was identified with, and was synonymous with the chosen people of Israel. It had been to Israel that God chose not only to reveal the self but also to make a covenant. An Israelite had to be proud of this election, and rightly so. It was a privilege to belong to this particular community. Moreover, it was through this community that the nations of the world were to be blessed. Understandably, the Israelites understood the kingdom to be theirs. It could not be taken from them, and they didn’t feel any need to do anything extra other than reveling in their privileged status. It was this complacency that Jesus wanted to challenge.
It can be that Jesus had watched how laid-back the people of the kingdom had become, or how they took their privileged status for granted. Israel had been placed by God as a light to the nations (cf. Isaiah 49:6), as a means of making God’s salvation reach the ends of the earth. Israel’s privileged position was a responsibility: they were to ‘do’ something.
Jesus’ described the onset of his ministry as the the ‘ushering in’ or the ‘inauguration’ of the kingdom. He had come to put the kingdom into a forward gear, so to speak. Jesus was not coming go take the kingdom away from the elected nation. His mission was to show them how to be worthy members of the kingdom. The Israelites could not claim the kingdom and at the same time remain inert. The presence of the kingdom had to be felt. This was the only way through which God’s salvation would reach the ends of the earth.