A binary star is a star system consisting of two stars orbiting a common center of mass. Systems of two or more stars are called multiple star systems. Actually most stars are in binary systems. Perhaps up to 85% of stars are in binary systems with some in triple or even higher-multiple systems.
Eclipsing binary stars
The brighter star is classified as the primary star, and the less shiny of the two is the secondary (classified as A and B respectively).