Finally we come to the goods. What was Jesus talking about when he preached about the Kingdom of Heaven? I believe that Jesus wanted to show us an ideal, a radical departure from the then current rule of the Romans and the Sanhedrin, with every person accountable to God, and submitting to one another.
This is a big topic, and I just want to look at a few elements of it for now. I will once again go over some historical context, and then take a look in Luke 6:20-49 to see what Jesus can tell us about the new kingdom.
We have in the Old Testament and ancient Jewish sources a form of writing called the covenant (I say writing, because we of course only have the texts. The form is almost certainly originally an oral agreement, not a written one). Probably the best example of covenental writing is the book of Deuteronomy, as well as some of the extrabiblical writings of the dead sea scrolls. A covenant is an agreement between a group of people that gets the seal of approval from God. Usually it is in regards to how they are to interact with each other, and the writings take a very distinct Jewish form. They start with a proclamation of the power of God's deliverance by remembering the way he delivered them out of Egypt, or remembering some other incident of God's saving power. After that they will go on to lay out the laws for their society. Finally, there will be a proclamation of blessings to be attained by following the covenant, as well as curses layed out for those who fail to follow the covenant.
A shorter version of a covenant can be seen in Joshua 24. It is a dialogue between the people of Israel and Joshua, and all the main elements are there pretty clearly. In verses 2-13 you have the reminders of deliverance. After that you have the rules of the society he is laying out (fear the LORD, throw away your idols). The blessings part is missing, however the occasion of the covenant makes the blessings inherent, land and prosperity in the promised land. The curse can be seen in ver. 19-20. One thing that is interesting to note in this passage is the voluntary nature of the covenant. It was an agreement that was entered into by each family by choice, not a mandate for living in the area.
In Luke 6 (as well as the sermon on the mount) Jesus is laying out a new covenant with the people he is talking to. If you read the passage closely, he is paralleling all the aspects of an ancient covenant, but in a slightly tweaked form. I believe that the prevalence of these speeches in Luke and Matthew gives us a view into what Jesus' ideal is for people's interaction with each other. I won't go verse by verse, because it is a pretty long section, but I do want to highlight some things.
In verses 20-26, we have a modernization of the practice of calling to mind God's deliverance. In ancient israel, when the people were in their promised land, it made sense to hearken back to the times of God's saving power, that He brought them into the rest they experienced. But for Jesus, in his day, there was trouble all around, and it didn't help that God had once done things. Instead, what he does is to call to attention the future deliverance of God in the coming of the Kingdom of God. If you like more theological terms, he is acknowledging the immanent eschaton. Instead of looking back and saying "see how God delivered us from the hands of the Egyptians and brought us to a land of His choosing" he is saying, "This current suffering will shortly be done away with in God's coming deliverance. The fortunes of men will be reversed, the present age will pass away, and God's kingdom will come into power." Note the blessings and woes, a contrast between how things are in the present and how they will be in the near future.
In verse 27 there is a shift. "But to you who are listening I say:..." Here Jesus is changing the focus to the substance of the covenant(v. 27-45). In Matthew we have a much expanded version, but most of the main points are here as well. Do good and be just, regardless of what the other party is doing. Do not judge and help one another. These all relate directly to our social and political interactions. Jesus is calling us to live out the Kingdom, even before it comes. It is a call to hasten the coming of that kingdom by enacting it on earth. This is the covenant that Jesus is inviting us into, an agreement to choose how to live our lives, with a view towards other people. In the times of Jesus, like today, the poor and downtrodden were falling through the cracks. There were no "social programs" that the government enacted to help the less fortunate. The only hope for those with nothing was charity from their neighbors. Jesus is calling for that to happen, for his followers to voluntarily agree to live out the kingdom in the fallen world.
Note the section on cooperation, and judging others(v. 37-42). In these verses Jesus is encouraging a new system of leadership based on experience instead of authority. We are no longer to be rulers and judges over other people, but to aid them in things we have learned, but that they still struggle with. This is the point of removing the plank in your eye before helping your brother remove his speck. It is also present in the student not being above the teacher, and the bit about the blind leading the blind. All over the place in the Gospels we have this idea of the servant leader. Jesus has no use for a leader who tells people what to do, but instead desires leaders who will teach by example, lifting their fellow man up to their level, so that all can live in peace with one another.
The final portion of a covenant is the blessings and curses for following or not following. This is to ratify the agreement, similar to a binding signature, with God as the person who is binding it. Jesus tweaks this part a little bit, but not much. Verses 46 through 49 comprise this part of the covenant. Jesus here is not compelling anybody to follow his words, merely stating the consequences for regarding or disregarding his words. The Kingdom is coming and nobody can stop it. The wise man will heed the words of Jesus and willingly become an instrument of the kingdom.
In conclusion, we have now seen the ideal kingdom of God as explained by Jesus. There are no earthly rulers, only leaders who can help others by virtue of their experience. The poor and downtrodden are looked after by the willingness of the well off to put the welfare of the needy above their own. We have a kingdom where God is the ruler, no earthly man, much like the ideal that was in place before Israel sinned by asking for a king. Jesus lays all this out in covenant form, recognizable by the people of his day as a voluntary contract between the individuals involved, and to be followed regardless of what is being done by those not beholden to that covenant.