Chesterton's fence is the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood. The quotation is from Chesterton’s 1929 book The Thing: Why I am a Catholic, in the chapter entitled "The Drift from Domesticity": "In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it 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."
There are a couple of problems here. The first is that, over time, the reason a very useful institution was created may get lost so that no one really knows why it was created or how exactly it is useful, or it may have developed empirically over centuries or millennia to be the best way of doing things but no one ever fully articulated the reasons why. When the modernizer challenges it, the conservative isn't ready with a good explanation, and the modernizer then assumes there isn't one.
Another issue is that Chesterton's statement of his maxim assumes the conservative (i.e., "more intelligent") reformer has the power to stop the modernizer, but that's often not the case. Often in society both put their arguments out there and a bunch of fence-sitters cast the deciding votes.
As a result, some important American institutions have been torn down in part because conservatives seemed unable to adequately explain their purpose. When they tried to preserve them, they seemed tied to dead traditions, stupid, or bigoted. Decades later the negative effects of the destruction become apparent; in hindsight we can see the purposes of those institutions fairly clearly, but we can't go back in time to deliver our now-learned retort.
Some human institutions, like government, are consciously created and we have something like the Federalist Papers that explains them. However, some are not consciously created. They developed empirically, by accumulated experience, over many generations. That's what living tradition is, the accumulated experience and wisdom of a culture.
Wisdom, though, can be ineffable. Sometimes you know something is right, but you cannot intellectualize why. That is the problem in miniature: How can we tell the difference between ineffable wisdom and baloney? It's a difficult problem.