The books of Matthew, Mark, Luke, John, and the beginning of Acts are filled with what the authors purport are statements of Jesus. Jesus is quoted as making several statements about "the Kingdom of Heaven" or "The Kingdom of God". Those statements are often given as parables that start with a phrase something like "The Kingdom of Heaven is like..."
So there are many statements of what this kingdom is like. Jesus command his followers to go out and preach about this kingdom. However, after all these years, I still can't tell you what this kingdom is supposed to be based solely on Jesus teachings. It seems that when professed Christians try to explain what this kingdom is they have to refer to books written by the apostles after Jesus' ascension to heaven.
Are there any statements purported to be from Jesus where he explains what this kingdom is?