The Department of Extra-Normal Operations, or simply the D.E.O., is a governmental organization led by Hank Henshaw, created following Kal-El's arrival on Earth to monitor extra-terrestrial presence on the planet.
Following Kal-El's arrival on Earth, the United States government decided that they needed to protect themselves against extra-terrestrial presence, and potential invasion, so they created the Department of Extra-Normal Operations. 24 years following, after Fort Rozz crashed on Earth, they began to catalogue of all of the aliens seen in public.
Twelve years later, they captured Kara Danvers. She was made aware of the department's existence, and their motives. Though they initially didn't work well, Hank Henshaw allowed Kara to take down Vartox, an alien threat, as Supergirl.