When you tell someone to get off his high horse, you are asking him to stop behaving or talking as if he were better than other people.
In the old days a person’s status was determined by the size of the horse he rode. Tall horses were ridden by royalty and noblemen. So when you tell a person to get off his high horse, you are asking him to stop behaving like royals or noblemen.
Examples: ”Ever since Sujata won the first prize for her short story, she’s been acting a bit strange. Someone must tell her to get off her high horse.” * ”Listen, we’ve been friends for a long time. Get off your high horse and talk to me”.