What are the visions that Paul saw?

“I must go on boasting. Although there is nothing to be gained, I will go on to visions and revelations from the Lord. I know a man in Christ who fourteen years ago was caught up to the third heaven. Whether it was in the body or out of the body I do not know—God knows. And I know that this man—whether in the body or apart from the body I do not know, but God knows— was caught up to paradise and heard inexpressible things, things that no one is permitted to tell.” 2 Corinthians 12:1-4

In 2 Corinthians 12:1-4 the Apostle Paul is unsure whether this remarkable experience included his body or took place separate from it. As much as it appeared to Paul that he actually went to the third heaven (God’s residence), we believe that he was caught up mentally and saw a vision of God’s abode and of the new condition of things as they will be under the spiritual control of Christ, or, as you mentioned, a glimpse of the third dispensation (the world to come). 

The inexpressible things that Paul heard were, most likely, the plans and purposes of God. He might have seen the events that would transpire up to the present time. He might also have seen what would happen during Armageddon and how God’s kingdom would come to be established on earth. 

Since he was not allowed to explain these visions, their meaning was a secret entrusted to him. These visions were most likely the same ones the Apostle John later saw and was permitted to express to the Church in symbols in the Book of Revelation. John’s revelation included the entire Christian age and its changing scenes of church and state, to the end of this present evil world, where he saw Satan bound, Christ reigning, and a new heaven (or spiritual government) and a new earth (society) established (Revelation 21:1).