Parsec stands for Parallax Arc Second, and is a measure of astronomical distances approximately equal to 3.26163626 light years. The parsec is a useful unit of measurement because it directly translates a measurable stellar phenomenon into a distance measurement.
Parallax is the name given to the apparent movement of an object against its background as the observer's viewing angle changes. As the Earth orbits the Sun, its viewing angle changes enough to cause measurable parallax with stars up to 1000 parsecs away from space based telescopes. Earth based telescopes are restricted by a reduction in resolution caused by the atmosphere, and can only measure parallax in stars up to 100 parsecs distant.
Parallax must be measured against an unchanging background, and because stars greater than 1000 parsecs distant exhibit no measurable parallax, these background stars are used for this reference. The parallax of the stars is measured in arcseconds. One caveat is that the stars appear to move across the sky over long periods of time, and this proper motion must be taken into account when measuring parallax.
Objects and distances in the sky can not be measured in centimeters or inches. Instead, distances in the sky are measured in terms of how much of the sky's arc they cover. For most objects, this is on the order of arcseconds — 1/3600 of a degree. The Sun, for example is about 1,900 arcseconds in diameter, and the Moon is only slightly smaller at 1,800 arcseconds. One arcsecond is just over one mile on the Moon as seen from Earth.
The parsec is defined as the distance to a star with a parallax of one arcsecond when the viewing position changes by one astronomical unit (AU). This means that the parallax should be measured over one quarter of the Earth's orbit so that a right triangle is formed between the Sun, the Earth, and the measured star. This is one half of the maximum possible parallax observable over a full six month period.
b r s Earth
a o t
c u a
k n r Star∠ Earth Sun
Distances not to scale, ∠ represents the parallax angle
Because the distance from the Earth to the Star is on the order of light years, and the distance from the Earth to the Sun is on the order of light minutes, this is a very narrow triangle (with an angle measured in arcseconds), and the small angle approximation applies with virtually no reduction in accuracy. This simplifies the math to:
d = --- where "d" is in parsecs and "p" is in arcseconds.
For example, the closest star to the Sun, Proxima Centauri, has a measurable parallax of about 0.77 arcseconds, so it is about 1.3 parsecs, or 4.2 light years, away.
The idea of stellar parallax was first proposed by the Greek astronomer Hipparchus (190–120 BC), most famous for developing the apparent magnitude classification for the brightness of stars. The heliocentric and geocentric theories of the solar system were being debated at the time, and Hipparchus realized that if the Earth did indeed orbit around the Sun, there should be observable parallax in the stars, assuming the stars are not infinitely far away. Unfortunately, without the aid of telescopes, Hipparchus was not able to measure any parallax in the stars and concluded the geocentric model was correct. The unaided human eye has a resolution of about 60 arcseconds (opinions vary widely), far too large to detect stellar parallax. By comparison, the Hubble Space Telescope has a resolution of about 0.05 arcseconds (20 parsecs, or 65 light years) (to put that in perspective, there are about 1,000 stars within 50 light years, 133 of which are visible to the naked eye).
Friedrich Wilhelm Bessel
It was not until 1838 that the German astronomer Friedrich Wilhelm Bessel was the first person to be able to measure stellar parallax, using a Fraunhofer heliometer. He chose the star 61 Cygni to measure, reasoning that a star with a large proper motion would be relatively close to the sun, and therefore have a large, measurable parallax — he measured its parallax as 0.314 arcseconds, placing it at 3.18 parsecs, or 10.3 light years (its actual parallax, measured with modern equipment, is 0.292 arcseconds, 3.42 parsecs, 11.2 light years).
In honor of Hipparchus' many achievements in astronomy, the High Precision Parallax Collecting Satellite (Hipparcos) was named for him (sort of). The Hipparcos satellite ran from August 1989–August 1993 and, among other things, observed parallaxes for about 2.5 million stars, out to a distance of about 1000 parsecs.