Esther,
You asked:
What is the "The secret of the kingdom?"
First, we need the definition of the word "secret", which is the Greek word:
MUSTERION
In part from Studylight.org
http://www.studylight.org/language-studies/greek-thoughts/index.cgi?a=3
...The fundamental meaning of the word therefore has to do with information known only to those on the inside, but hidden to those who are without.
Secondly we need to consider the words: "has been given" which is from the single Greek word: DIDOTAI
DIDOTAI being the Greek "perfect" which indicates a completed action the results of which stand as accomplished and are in effect at the present and continue to be so.
In the grammatical notes of Spiros Zodhiates' Complete Word Study New Testament he states concerning the perfect "tense":
"The Perfect describes an action, or more correctly, a process, that took place in the past, the results of which have continued to the present."
Considering that this statement of Jesus was made when he was alone with some around him including the twelve and that Jesus has in other places made it clear that he has come to Israel, even the lost sheep of Israel; we would, it seems to me, have to conclude that is some respect he is here speaking (at this moment) to a small contingent of Israel...why ?
Because of this word DIDOTAI !
The phrase "The kingdom of God" is in the genitive case in Greek which modifies in this case the word "MUSTERION"; that word that we now know means that some have had, that is, been given as insiders, information not generally known. The kingdom of God, that is, tells us what "kind of" MUSTERION we are dealing with.
Israel, as the people chosen by God have been given many things that communicate what is characterized by "The kingdom of God", that is, the reigning, the realm of and having to do with what is "of God"; that's the genitive case. What is "of" the kingdom...what is "of" God.
Consider the whole of the Old Testament including the Tabernacle, the Law, the Temple, etc. All of these things are portraying for us how God, ultimately through His Christ, might include us and bring us to Himself, and bring Himself into us. Consider for one thing, that upon the death of His Christ, the veil separating us from God and He from us was torn open from top to bottom, thereby representing an open way. An open way for any who would approach, to access God and He them.
This all, I would contend, is the MUSTERION that had, through the process of all that preceded Jesus, as is contained in God having dealt with Israel; this, is what Jesus referred to as being the MUSTERION that is what is characterized, by what is "of" the kingdom, of what characterized, by what is "of" God.
This is perhaps why Jesus exclaimed to Nicodemus concerning Nicodemus' not understanding being born from above: "Jesus answered and said to him, You are a teacher of Israel and you are not understanding these things?"
It would seem that Jesus expected Nicodemus to be an insider, an insider that should have been familiar with what is contained in the MUSTERION, the MUSTERION that Israel had been privileged to be privy to.
A few examples:
In Leviticus 10:3 Moses said to Aaron, Aaron of course being set apart for priestly function, "This is that the Lord spoke saying, I will be sanctified in them that come near Me," that is I will be sanctified or set apart in the hearts of all the priests. Priests were known then as those who drew near to God.
In Ezekiel chapter 43 we find a similar insight in verse 19. It talks about the priests who approach unto Me to minister unto Me. In other words, God again identifying them as those that drew near to His presence. Again in chapter 44 of Ezekiel and verse 13 it speaks of priests again as those who come near to Me.
So in the Old Testament then, those who drew near were the priests and before they could draw near they had to have washed and cleansed themselves, hands and feet. They had to have offered sacrifices on their own behalf and had a right relationship with God. And ceremonially being clean they could come into the presence of God under the regulations of the old covenant representing the people.
(the previous 3 paragraphs are in part from a message found at Grace to you and John MacArthur...http://www.gty.org/resources/sermons/59-25/drawing-near-to-god-part-2)
So then, The secret of the kingdom ? I would suggest that it is anything and all things that communicate to an insider, information and direction concerning God and how He intends to be involved towards, with, and into us and we to Him.
For me, this gives fresh emphasis to something Jesus said:
"I am the way, the truth, and the life...no one comes to the Father except by means of me"