A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primaryand the other is its companion star, or secondary. Research between the early 19th century and today suggests that many stars are part of either binary star systems or star systems with more than two stars, called multiple star systems. The term double star may be used synonymously with binary star, but more generally, a double star may be either a binary star or an optical double star which consists of two stars with no physical connection but which appear close together in the sky as seen from the Earth. A double star may be determined to be optical if its components have sufficiently different proper motions or radial velocities, or if parallaxmeasurements reveal its two components to be at sufficiently different distances from the Earth. Most known double stars have not yet been determined to be either bound binary star systems or optical doubles.
Binary star systems are very important in astrophysics because calculations of their orbits allow the masses of their component stars to be directly determined, which in turn allows other stellar parameters, such as radius and density, to be indirectly estimated. This also determines an empirical mass-luminosity relationship (MLR) from which the masses of single stars can be estimated.
Source: wikipedia, NASA