The first heaven is the sphere where the clouds move across the sky. This is also called the firmament in the Bible.
The second heaven is the sphere where the sun, moon, and the planets move across the sky.
The third heaven is the sphere where the stars move across the sky.
How do I know this, you might wonder. The answer is through simple logic. Just study the sky for yourself, and you will see the three spheres. See how the clouds move in the first sphere, the firmament. Then behind them, in another track, you will see the sun move.
The three heaven/sphere model is a primitive variant of the later seven or multiple sphere cosmological model, developed by ancient people.
(The clouds move in one track, the sun moves in another track. Both the clouds and the sun are in the sky, but there's a difference. The sky is clearly divided in some way; you can see and understand that there are more than one sphere, in heaven.)
Then in the early evening, you will see the moon and the planets move in the same direction as the sun, and must conclude that they belong to the same, second heaven. Then later at night, you will see that behind the moon and the planets, there are stars moving along another track, across the sky*. You will then naturally refer to that sphere as the third, or simply, the third heaven.
Let's not complicate the Bible. It was written to be understood by simple people. And like Albert Einstein said: True things are simple.
If you adopt this simple view, it will open up some very interesting avenues, in the rest of the Holy Scriptures. All in line with and illuminating the same Scriptures.
* And that's why they called certain "stars" planets, wanderers, as they moved differently from the other stars.
(Of course, you have to watch them more than one night, to see their path differ from the fixed stars, but people knew about this very early in human history.)