The clock on your wall is set according to mean solar time. It is natural to want to keep time according to the Sun's motion, yet astronomers find it more useful to use yet another time. Astronomer's use sidereal time, which is based on the stars rather than Sun. In fact it is impossible to walk into an observatory and not find a sidereal clock. In more astronomical terms sideral time is just the right ascension of any object on the meridian.
Siderial time is really only useful for astronomers or sailors.
In fact a sidereal clock and an ordinary clock tick at different rates because they are based upon different astronomical objects. Sidereal time is tied to the position of the vernal equinox, because that is the point from which right ascension is measured.