Astronomer Royal was originally the title of the director of the Royal Greenwich Observatory, but since 1972 it has simply been an honorary title. Note that the Astronomer Royal for Scotland is a separate title.
King Charles II, who founded the Royal Greenwich Observatory in 1675 instructed the first Astronomer Royal John Flamsteed, "to apply himself with the most exact care and diligence to the rectifying of the tables of the motions of the heavens, and the places of the fixed stars, so as to find out the so much desired longitude of places for the perfecting of the art of navigation."
The complete list of Astronomers Royal is given in the table below.