From Glossary of Meteorology
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  1. The greatest distance in a given direction at which it is just possible to see and identify with the unaided eye 1) in the daytime, a prominent dark object against the sky at the horizon, and 2) at night, a known, preferably unfocused, moderately intense light source.

    After visibilities have been determined around the entire horizon circle, they are resolved into a single value of prevailing visibility for reporting purposes. There are inherent difficulties with the conventional requirement that visibility markers be both detected and recognized. The more rigorously defined concept of the visual range avoids reference to recognition; thus, if the recognition requirement were dropped, the visibility could be defined as a subjective estimate of visual range. For most practical purposes, it can be defined that way now. Daytime estimates of visibility are subjective evaluations of atmospheric attenuation of contrast, while nighttime estimates represent attempts to evaluate something quite different, namely, attenuation of flux density. Thus, visibility data must be regarded as falling into two distinct classes, those obtained by day, and those by night. In U.S weather observing practice, it is the value as obtained and reported by an observer or by an automatic weather station.
    See surface visibility, control-tower visibility, runway visual range, night visual range.

  2. The clarity with which an object can be seen.