Typically the Planar is used either to denote a lens design, or when referring to a line of Carl Zeiss lenses that utilise the planar lens design.
The original Planar lens design is a further development of the symmetrical double-Gauss lens design with six elements in four groups and was first developed by Paul Rudolph in 1896 while he was working at Zeiss in Germany.
Illustration of the Planar design, By Tamasflex – Own work, CC BY-SA 3.0
The Gauss and double-Gauss principle behind the Planar design was by no means new (originating from the early 1800’s), and had been used extensively in telescopes, but Rudolph’s calculation from the late 1800’s produced a lens that showed very low coma and astigmatism and produced a very level focal plane (thus the name Planar). Moreover, the design had high potential for sharpness as well as allowing for wider apertures than other contemporary designs.
Problematically, in the era before lens coatings, the higher number of lens groups (compared to e.g. the Tessar designs) led to a lens exceptionally prone to flaring and loss of contrast. Subsequently, the design was shelved for roughly half a century.
With the advent of modern coatings the design was resurrected and has – with modifications – become the standard approach to designing fast normal and short telephoto lenses.
Read more (elsewhere):
The history of the Zeiss Planar (at vintage-camera-lenses.com)
The Double-Gauss lens (on Wikipedia)