Astrometry is a part of Astronomy and deals with the positions of stars and other celestial bodies, their distances and movements.
It is one of the oldest subfields of the science, dating back at least to Hipparchus, who compiled the first catalogue of stars visible to him and in doing so invented the brightness scale basically still in use today. In 1750, Simon Newcomb founded modern Astrometry.
Apart from the fundamental function of providing Astronomers with a reference frame to report their observations in, Astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. It is also instrumental for keeping time, in that UTC is basically the atomic time synchronized to the Earth's rotation by means of exact observations.