It usually means that someone has taken a position or made a statement. When they are challenged on their position or statement instead of 'backing down', they 'double down' on the original position or statement by committing to it more strongly than before. Example: Mr. Ahmadinejad expressed doubt that the Holocaust ever happened. When confronted by the press about this statement, instead of back-tracking he 'doubled down' on his original statement by saying that he was quite certain there had been no significant persecution of Jews in Europe ever.