I know she doesn't look much like it in that photo, but Betty, AKA The Kings Bet, is a thouroughbred racehorse. The brand is the stable in which she was born, and she has another on her other shoulder giving her birth year.
Please don't worry about this having hurt her, the branding is done with liquid nitrogen these days, not hot irons. It is painless and makes the hair turn white, rather than scaring the skin.