A DQ is short for a disqualification.
The rules of horse racing limit what horse and rider can do to get to the finish line first. In essence, if a horse veers in front of a horse making a move or changes paths and bumps a competitor, it can be disqualified.
If the stewards, who monitor the races from an elevated viewing box as well as video feeds, decide the offender cost the other horse a better placing or finish position, they can disqualify the horse that caused the trouble and place him or her one spot behind the horse that was interfered with.
The decisions are judgment calls and are often controversial. The disqualification of The Wicked North in the 1993 Santa Anita Handicap immediately comes to mind, resulting in a DQ over a seemingly minor brushing incident at the top of the stretch. The owner appealed the decision, which cost The Wicked North the victory in the $1 million race, but it was upheld by the California Horse Racing Board.