It was a standard determined by Snellen, the inventor of the standard optometrist's eye chart. [0]
Snellen defined “standard vision” as the ability to recognize one of his optotypes when it subtended 5 minutes of arc.
Basically each line on the chart is marked with a distance such that it subtends 5 minutes of arc from that distance away. 20/20 simply means that you can see the 20 feet line from 20 feet away (20 feet being the standard testing distance). In no way does it represent "perfect" vision or the best possible resolution of the human eye.
Next time you go for an eye test you'll notice that the 20 line is usually the 3rd or 4th line up from the bottom. So if you can read lower than this your vision is "better than 20/20". This is often achievable with correction, even if your uncorrected vision is quite bad. (I believe there are limits to this with very high myopia, because of distortion caused by very thick lenses, etc).
This is why I find the way that LASIK is marketed to be disingenuous. I feel like people might be seduced by the offer of "20/20" vision, not realising that they already see better than that with their glasses on. The fact that LASIK companies are not 100% upfront about this just makes me a little suspicious about what else they might be hiding.
Disclaimer: I'm not an optometrist. Anyone who actually knows what they're talking about, feel free to correct me!
[0] https://en.wikipedia.org/wiki/Snellen_chart#.226.2F6.22.28m....