I enjoy giving simple clear concise answers to the questions that are often asked during the eye examination, and to some questions seldom asked. One of the most logical questions asked is "what does 20/20 mean".
I still find this question one of the most challenging to respond to. But before I struggle with the explanation let me say I find it a near meaningless description of vision. Vision is so complex and varied, reducing it to single number or fraction is about as effective as reduce a presidential candidate’s worthiness down to a single number. I have assisted a person in and out of my exam room because they were legally blind with severe tunnel vision, yet they could read the 20/20 line! Try looking through a straw and walk across room, you quickly realize how important peripheral vision is, yet you will be able to see the 20/20 line ... if you can find it.

That makes a good intro to the subject. Hold up an ice cream cone so you can see through the broken off tip of the narrow end. Everyone around you will stop in silence and just ponder your sorry predicament.
The arc seen from top to bottom of the cone is how many degrees it spans. If the "E" on the 20/20 line filled the cone top to bottom, the cone would give you a arc of vision of 5 minutes. I prefer to fill it with butter pecan.
Each degree of the 360° in a complete circle is divided into 60 minutes. If you can see 20/20 you can resolve 1 minute of arc (¹/₆₀^th of a degree). The 20/20 "E" casts 5 minutes of arc, each of the three fingers of the “E” plus the two spaces make a letter that casts a total of 5 minutes of arc.
Knowing it is an "E" means the person can resolve each component so they must be able to resolve 1 minute of arc. Notice that the fraction 20/20 equals one and the inverse of 20/20is also one.
If the best vision is 20/40 the person must observe something twice as big as 20/20 to see it. The inverse of 20/40 is 2, which means that person can resolve 2 minutes of arc.

Did I make myself clear? Well that is only the bottom number part of the 20/20. Look I told you early on this was all near meaningless so go do something else.
The top number indicates how far the chart is viewed from. Eye exams should be done using a 20 foot viewing lane using mirrors to achieve the 20 foot distance. So 40/40 vision is the same as 20/20 because both indicate resolving one minute of arc, but the 40/40 is achieved by seeing a letter at forty feet which is twice as big as the letter viewed at 20 feet.
Let me guess! You’re about to ask why we use 20 foot lanes? Give it up, you ask too many stinking questions. Do you know what optical infinity means? It is the distance an optical system no longer needs to be refocused for. If it is focused at infinity objects close will remain in focus up to a limit. Well the human eye achieves optical infinity at about 16 feet. If an object is clear at 16 feet, anything further remains clear without adjusting the focus. So we could use a 16 foot lane but historically they used a 20 foot lane because they didn’t have the relentless patience to read this lengthy paper before they set up shop.
So what’s up with you to sit here and suffer through this longer than expected explanation? I feel bad for you. I really think your time would have been better spent clicking the fun stuff on my web site!