First of all, one has to distinguish between visual acuity (VA), which is a measure for the maximal possible resolution your eye-brain-system can achieve, and the refractive error, which measures the deviation of the optical system of your eye from emmetropy (=perfectly balanced optics, sharp focus on retina without any glasses) in diopters of spheres and cylinders and thus determines what corrective glasses you need to wear in front of your eye in order to achieve your maximum possible visual acuity.
Visual acuity can be measured without corrective glasses, i.e. the "native" VA of your eye, or with your best corrective glasses, which then gives you the value of your "Best-corrected visual acuity" (BCVA), and only this value is useful for comparison purposes, e.g. for driver's licenses (because errors that can be corrected by glasses also are to be corrected by law, as this is rather easy to do for everybody), and also for scientific evaluation of eye performance.
This also explains a common misconception: When somebody is very near- or farsighted (myope or hyperope), he has to wear glasses with a high (absolute) value of diopters, e.g. -7 dpt. But if he reaches 20/20 vision with his glasses on (again, BCVA), then to an eye doctor, this will matter the most; for the glasses are neglegible in comparison to "real" eye diseases which can impair your eye function and lower the BCVA your eye can reach. Many people incorrectly compare their eye functions by comparing the amount of diopters in their glasses, yet this doesn't really say anything about the maximum resolution their eyes have when wearing their best glasses. Refractive errors can be corrected by glasses, contact lenses and laser surgery, but the maximum visual acuity an eye-brain-system is able to achieve can not be altered in any (simple) way.
Now, when visual acuity is measured, a full visual acuity, i.e. "normal", or 100%, or any way you'd like to name it, has once simply deliberately been determined by a minimum angle of resolution of 1 arc minute, and the charts that are used for testing it have letters that correspond with this resolution. 1 arc minute of resolution corresponds to being able to separate two points with 2,91 cm between them at a distance of 100 m. Now note that this does not necessarily correspond with what most people are able to see; as said previously, the definition of 100% visual acuity was deliberate.
The capability to distinguish points with 1 arc minute of space between them has been defined as 20/20 (or 6/6) vision in Snellen charts, 1.0 vision in decimal charts (conversion table), and later 0.0 logMAR, which is the logarithm of the minimum angle of resolution and which has become the gold standard in measuring and comparing visual acuity (see p.13 for conversion chart), but is predominantly used for scientific purposes and less in clinical environments.
This is basic knowledge in optics, optometry and ophthalmology. Wikipedia describes the correlations between the terms pretty well.