This number is magically astronomical.
206265 is the number of arcseconds in a radian. It is also the number of Astronomical Units in a Parsec. Astronomers use this number all the time. They use it so much, in fact, that it is sometimes referred to as a magic number.
This is really just another number astronomers have to memorise in their war against standard units. Astronomers like arcseconds, and they hate radians. It is nothing more than a conversion factor, but if one happens to be an astronomer by trade1 then this is a very useful number.
Even if you're not an astronomer, you could still walk up to a local astronomer, greet him or her with a cheer of '206265!' and be welcomed to the nearest pub or symposium to discuss further intricacies of his or her line of work.