Chesterton's Fence says, in short, that you should never let someone reform something (a rule, an institution) if he tells you that the thing doesn't serve any purpose. The philosopher G.K. Chesterton vividly illustrated his idea by asking us to imagine a fence strung up across a road, representing any kind of law or institution that we might find odd or inexplicable. There's a certain type of reformer, says Chesterton, who
...goes gaily up to [the fence] and says, “I don’t see the use of this; let us clear it away.” To which the more intelligent type of reformer will do well to answer: “If you don’t see the use of it, I certainly won’t let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it."
Chesterton's Fence is a claim that every rule or institution you encounter probably exists for a reason. It might be a bad reason, an outdated reason, or even an evil reason, but the fence didn't just appear out of nowhere. As Chesterton put it,
[The] fence did not grow there. It was not set up by somnambulists who built it in their sleep. It is highly improbable that it was put there by escaped lunatics who were for some reason loose in the street.
More than that, any institution or law that actually exists was set up, at least somewhat deliberately, by a Thinking Person with some kind of aim in mind.
Some person had some reason for thinking it would be a good thing for somebody. And until we know what the reason was, we really cannot judge whether the reason was reasonable. It is extremely probable that we have overlooked some whole aspect of the question, if something set up by human beings like ourselves seems to be entirely meaningless and mysterious. There are reformers who get over this difficulty by assuming that all their fathers were fools; but if that be so, we can only say that folly appears to be a hereditary disease. But the truth is that nobody has any business to destroy a social institution until he has really seen it as an historical institution.
In other words, if someone walks up to the fence and says "this doesn't serve any purpose" then she clearly doesn't understand the fence (the law, the institution), why it was created and who it serves. So she is also not going to understand the consequences of tearing it down, and she won't find other ways to fill or replace or remedy the needs that the fence once met. While Chesterton's Fence is often associated with a kind of conservatism, it's actually a super-useful concept for anyone at any spot on the political and philosophical spectrum: if you want to change or replace something, first remember that it was created for a reason and if you don't understand that reason then you ought to find it out first.