Ephesians 3:1-6

For this reason I, Paul, the prisoner of Christ Jesus for the sake of you Gentiles—

(v1, NIV)

Paul was just talking about unity in the body of Christ. The Gentiles were separate from God and God's people and were called the "uncircumcision" by what is the circumcision. However, they have now been brought near by the blood of Christ Jesus. Therefore, both Jews and Gentiles now have a way to be brought into the household of God. Paul begins to talk about something else that is linked to what he has just said. However, he cuts himself off and does not continue that train of thought. Verse 1 begins something new, but he does not continue it in verse 2.

Surely you have heard about the administration of God's grace that was given to me for you,

(v2, NIV)

God is administering grace. This grace is the grace by which we are saved in chapter 2 verse 8. He is the one who administers the grace which is a gift. It is up to us to accept his gift offered to us. Paul is speaking to Christians who must have heard of the administration of God's grace. They are saved and receivers of this grace, so it only makes sense that they have heard of and know about this.

that is, the mystery made known to me by revelation, as I have already written briefly.

(v3, NIV)

A revelation is made known to Paul. The mystery is described by Paul in verse 6.

In reading this, then, you will be able to understand my insight into the mystery of Christ,

(v4, NIV)

Reading Paul's letter will help them to understand Paul's insight into the mystery of Christ. Somehow his words are going to give them understanding upon reading them. I would assume that he means that he is going to explain to them his insight in a way that they would be able to understand. That is what I would understand from reading that. Maybe the mystery of Christ is very simple, or maybe Paul just does a really good job at explaining it.

which was not made known to men in other generations as it has now been revealed by the Spirit to God's holy apostles and prophets.

(v5, NIV)

People beforehand did not understand this. It wasn't even known to them. This has now been revealed and has not been revealed to people before. It was revealed by the Spirit. It would make sense that people beforehand did not know because people beforehand did not have the Holy Spirit. However, we do and at that time God had just given them the Holy Spirit.

This mystery is that through the gospel the Gentiles are heirs together with Israel, members together of one body, and sharers together in the promise in Christ Jesus.

(v6, NIV)

Paul refers to something which he calls the mystery. The mystery is described in verse 6. It is that the Gentiles and Jews are both heirs through the gospel and sharers in the promise of Christ Jesus. He talked about how the Gentiles were being brought near in the last paragraph.