The Visual Double Star Program at the USNO
Since the original 1846 charge to the first Superintendent, Matthew Fontaine Maury, the U.S. Naval Observatory has been engaged in the observation of double stars. The reasons for their importance fall under two broad categories:
The majority of stars in the sky are part of double or multiple star systems. The only way to determine stellar mass, the most fundamental property of a star, is through analysis of binary star systems. While stars similar to the Sun are known well, the most common stars, Red Dwarfs, and those that have the greatest impact on Galactic Evolution, the Massive OB stars, are not well determined.
While double or multiple stars are broadly characterized as more abundant than single stars, how different subsets, either based on stellar type or environment, may be enhanced or not can have significant implications for the evolution of the Galaxy. Unknown binaries could be responsible for a significant amount of the "missing matter'' of the Universe.
The coeval nature of binary stars makes them insolated sets which can be studied together. While the individual stars may be different, they are of at least approximately the same age and have the same chemical composition.
Binary stars are not only the predominent stellar evolutionary track, but they are a boon to astronomers for the plethora of data that can be determined from them.
Astrophysical questions relate only to pairs which are physically associated with each other: the true binary stars. However, for navigational purposes two stars which appear to be near each other in the sky but which not physically related are also a concern.
Determining the effective "center of light" of a close pair of stars may depend on many factors: type of detector used, colors of the stars, angular distance between them and any motion one star might have with respect to the other. For this reason, double and multiple stars have the navigational nom de guerre: Vermin of the Sky.
Simply avoiding double stars is not an option, as they are the predominent type of celestial object and new pairs are discovered every year. Furthermore, the brightest stars, which would presumably be best for navigation, are preferentially members of double or multiple star systems.