What was the purpose of the fence in Chesterton's Fence?

It's a hypothetical fence, its purpose is unknown. That's part of the point of the story, though. Don't rush to tear down a thing just because you don't know its purpose.

If abstract and hypothetical thinking doesn't do it for you, here's a real-world example: A colleague recently bypassed a step in out-processing employees (someone retiring in this case). The step, as written, was "Email such and such for the latest version of some form." Well, the latest version was clearly posted on SharePoint, why bother emailing when it's right there? So he obtained the form, and kept on trucking. A couple months later, though, he found out there was a problem.

It turned out there was a missing detail in the process documentation: email such and such for the latest version of the form, also they'll start another process that no one ever told you about that marks the person as not-an-employee so they stop getting paid.

Oops. Don't tear down fences too hastily, figure out why they are there first, then tear them down. Again, if that's too abstract, in this case update the out-processing documentation so it states the real reason why that person needed to be contacted, and also remove the nonsense about it being to get the most recent version of the form. Just point people to SharePoint for that.

I was once in Marseille, where there is a big Ferris wheel in the port.

My friend and I bought tickets to ride it at a kiosk, then walked up to the attendant checking tickets, who was standing directly in front of the Ferris wheel.

The attendant took our tickets, ripped a small notch on them, and then gave them back to us.

My friend asked, “What was the purpose of ripping the tickets and giving them back to us if we immediately get on the ride now?”

The attendant answered: “So you would ask me why I ripped it.”

The moral of this cryptic story being: the purpose of the fence may simply be to remind you to ask why it’s there.

The idea is don't tear down the fence until you know why it's there. But a fence across a road - it's so obviously wrong everybody wants to tear it down - not recognizing somebody with a good reason put it there. Big lesson when examining legacy code.

Then there is the Terry Pratchett version, when they move a big piece of furniture to reveal a door with a sign, "under no circumstances should this door ever be opened. " so they open the door and general madcap laughs ensue.

I think it was an imaginary scenario that Chesterton invented to illustrate a point.

There are some preparedness-paradox stories in the book A Libertarian Walks Into a Bear where people who weren't used to living near bears pooh-poohed¹ precautions against them that other people said were necessary. Some of them had never before seen why those precautions might help anything.

¹ Heh.

Somewhat related is the idea of "metaphorical truth", something that isn't strictly true, but if you act like it is, you'll be better off.

Example: All guns are loaded

I know the fence is there not to be torn down. It’d just be a better story (to tell others) if the fence actually had a purpose that could be revealed, so the listener could finally understand the value of the fence, and therefore the value of the approach of not tearing it down without understanding its purpose.