ryman,
As Dave and John was saying, when you finish reading and studying more, the Lake of Fire series will clarify this more for you. But to answer this question...
"When Jesus talks about not entering his kingdom, what exactly is he saying? From some reading I understand this to be a temporary thing of rewards and judgment?"
We have to remember the "IS" was and will be part of scripture. God is living and active, His word "IS"... and He lives His word out in us each person at their appointed time.
Luke 17:21 neither shall they say, Lo, here! or, There! for lo, the kingdom of God is within you.
John 3:5 Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God.
Most put "the kingdom" out there somewhere else, but we know that the kingdom of God is within us. The kingdom is not a physical place that we go to, it is a preparing our hearts to take on the mind of Christ within each person at their appointed time. When Christ comes to us He judges us, and as the old man dies the new man "spiritual man" is born within us. This is an AGE LASTING process, this is not instantaneous (no ten second salvation prayer and your done). The process of the kingdom being worked out in us... is a daily process. I die daily.
The old man, carnal man within us will never inherit the kingdom of God. That old carnal man will be destroyed by the brightness of His coming. This happens to the elect now... and the rest of mankind later at the great White Throne Judgment.
I hope that helped!