Chapter three seems to be about listing the names of those who helped with the building of the wall of Jerusalem and even mentioning those who didn't help. Here are just a few notes on what I believe this chapter is about.
One thing that came to mind was that nothing in God's Word is in vain. Meaning, that even the lengthy lists of genealogies and details have special purpose. So I cheated and googled that thought. Because specific names of gates and areas are mentioned, I thought it would be a good idea to have a diagram of Jerusalem to see where these places and names fit in.
On that note, here's what I saw in chapter three and after that is the link that gives an idea of what all of the details may mean.
In verse one we are told that Eliashib, who was the high priest, with his brethren the priests, built the sheep gate and sanctified it, as well as setting up the gate's doors. They also blessed the tower of Meah, and the tower of Hananeel I am guessing that each gate or area has a significant meaning which means, I looked it up and found some interesting notes and diagrams at a sight linked here (incase you are interested)
The rest of this chapter tells us specifically, who built what and who didn't.
There was the fish gate that was rebuilt, as well as…
Fortified the bros wall of Jersusalem
The valley gate
The Dung Gate
The gate of the fountain
The Tekoites repaired but their nobles did not.
As mentioned, the gates of Jerusalem have both a personal and prophetic aspect. I’ll use a table to display this so that you can read which ever column you want.
The Gate of Jerusalem Personal Significance Prophetic/Historical Significance
the House of Eliashib
the Water gate
the Wall of Ophel
The priests their own houses
the East Gate
Individuals repaired their own chambers and homes
The gate Miphkad
Here is the article the diagram was taken from if you want to hear someone's interpretation about Nehemiah's Jerusalem (click here).