Two stars in orbit around each other, held together by their mutual gravity. It's like two balls (of burning gasses) connected by a stick (gravity) that's spinning in the middle, except it's not at the middle, it's at the centre of gravity. Somewhere around 5-10% of the stars be can see are binary stars. There are several classes of binary star systems:
Binary stars are extremely useful because we can find their distance easily using spectroscopic parallax, or other methods. Additionally some binary systems appear have black holes in place of the stars. Half of the stars in our galaxy are in binary systems.
Also called "Double Stars".
The New York Library Science Desk Reference
A few websites from long before we kept reference listings. (Good ol' E1)
Astronomy with Dr. Martin Bier (great teacher) and the textbook Horizons by Michael A. Seeds