"Aurors are Dark-wizard-catchers, who work for the Ministry of Magic."
An Auror is "a Dark wizard catcher". They are an elite group of witches and wizards, loyal to the Ministry of Magic , whose mission is to fight against and capture the forces of the Dark Arts.
Aurors are like a police force, and sometimes work as intelligence agents. They have the authority to arrest malefactors like Death Eaters, and at times have been given authority to use deadly force against Death Eaters in particular.
When we are first introduced to the office, Death Eaters are already gaining force in the Wizarding world, so the Aurors' mission is clearly defined. It is not as clear what the Auror department does when there is no center of Dark forces to fight; one gets the impression, however, that they continue to work as sort of an elite police group, a magical SWAT team of sorts perhaps.