Visibility is an estimate of a distance you can see an object. Visibility measurements used to be taken by actual people everyday, but now they are taken at weather stations that have an automatic sensor. At some airports, the observation is still made by a person, but there are now more automated reports.
The sensor will send out a column of light to a detector a few feet away. The detector will then determine if its a clear day, if there is fog, or if precipitation is reducing visibility.
This automatic sensor figures this out by determining how much light was absorbed. On our weather maps we use ten mile visibility as the number to show it is clear, if it is reduced, the number will be lower than ten.
Sensors can be pretty accurate, but they have their limitations. It is always helpful to have human eyes letting us know if it is foggy or not. We welcome any visibility reports each day!