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It’s a phrase that comes from written (and later, printed) text.
Pull up any document, written, printed, or digital (like a PDF or a Word doc). On just about any one of them, there will be a border all the way around the page where no text is written. That’s the margin. By convention, we leave it blank to make the page easier to read. If you want to be “correct”, you don’t write anything there.
However, if you *reeeeeeally* needed to just barely complete a word, and you don’t have enough room to fit the whole spelling inside the border, you *cooooould* fudge it out into the margin. Just this once. It’s not like it’s the edge of the paper, there’s still paper *there*, right? You’d prefer to not have to use the margin like that, but if it becomes necessary, it’s available to you.
And that’s basically the whole concept of a “margin of error”. If you are doing a thing where you’re expected to stay within some explicit range, and for a short moment you need to go a small ways outside of that range, you have a buffer zone that lets you do so. It’s technically an error to be outside the margin, but it’s not the end of the world.
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