The word Binary tells you there must be two stars involved. These two stars, together in a system, revolve round some common point. This point is the center of mass according to Kepler's Laws.
If you can see the stars through a telescope, they are called "visual binaries".
If they cannot be seen as individual stars due to their proximity to one another, they are called "spectroscopic binaries".
To discover if we are looking at a binary system, we must use "periodic Doppler shifts of the wavelengths of lines seen in the spectrum". If two lines show up, it is called a "double-lined spectroscopic binary". Most of the time only one line shows, however, and this is called the "single-lined spectroscopic binary.
Another type of binary system is the "eclipsing binaries". With these, they are situated so that to those looking or the spectroscopic lines, one will pass in front of the other blocking it's light, just as an eclipse of the Sun works.
Quite a few of the stars we see in the night sky are binary stars. Binary stars are helpful to astrologists in determining the mass of a star. They use the "laws of celestial mechanics" to measure the two stars orbit, size and speed, giving the means to calculate the mass.
So next time you look out at the sky, remember that half the stars you may be looking at are binary stars instead of single stars. Either way, they are quite a sight in the night sky.
If you wish to have an understanding of Kepler's laws, you can access them from this site.