One of the most noteworthy references to kingdom can be found in context at Matthew 5:19: 17 ?Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven..

1. Jesus is being accused of breaking the Torah; Jesus says that, actually if truth be told, he is not breaking but fulfilling the Torah — bringing it to its divinely-intended goal. (He sees the Torah as the preliminary glimpse of God’s will and he is the fullness of it.) Notice again how central Jesus is.
2. Those who follow and teach Jesus’ teachings will be great in the kingdom; those who don’t will be “least” (which is a gentle way of saying “not at all”).
3. Kingdom is future; kingdom is entered in that future by following Jesus in the now.
4. To enter that kingdom one must not follow the Pharisees and scribes, or at least not behave as they behave.
What is kingdom here? Evidently, God’s society: king, king’s will as taught by Jesus, king’s people who follow Jesus, future society where it will all be right.