The following is a pretty thorough article (though verita's post seems pretty comprehensive):-
http://www.jesuswalk.com/manifesto/kingdom-of-heaven.htm
(see the entire article)
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But what does the phrase "kingdom of heaven" mean? Is it the same as the phrase "kingdom of God"? I've heard a lot of theories, but when you compare Matthew's gospel with the many parallel passages in the other Synoptics, Mark and Luke, you find that where Matthew says "kingdom of heaven," Mark and Luke say "kingdom of God." The explanation is this: Matthew was writing especially for a Jewish audience who were careful not to utter the name of God, lest they be guilty of breaking the Third Commandment, "to take the name of the Lord your God in vain" (Exodus 20:7). We hear people doing the same thing today. "For heaven's sake!" someone will exclaim. They've trained themselves to speak that way so as not to dishonor God.
When you see "kingdom of heaven" in Matthew, it means exactly the same thing as "kingdom of God" in the other gospels. It refers to the Reign of God which has come in the person of Jesus Christ himself, and will culminate in the coming of Christ and his reign on earth, the time looked forward to in the Lord's Prayer: "Thy kingdom come, thy will be done, on earth as it is in heaven" (Matthew 6:10). The Kingdom is now in the presence of the King in our lives through his Spirit, yet we look forward to the future when that "earnest of the Spirit" (KJV, 2 Corinthians 1:22; 5:5; Ephesians 1:14), that downpayment we've received, will be completed when the King returns and establishes his kingdom on earth where there was once human resistance and rebellion.
References to the Kingdom in the Sermon on the Mount
"Blessed are the poor in spirit,
for theirs is the kingdom of heaven" (5:3).
"Blessed are those who are persecuted because of righteousness,
for theirs is the kingdom of heaven" (5:10)
"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. 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" (5:19-20).
"... Your kingdom come,
your will be done
on earth as it is in heaven" (6:10).
"But seek first his kingdom and his righteousness, and all these things will be given to you as well" (6:33).
"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven" (7:21).
The above is Biblical; my own interpretation (and I know one or two who agree with me), we will all enter the kingdom of heaven, in time.