Five-card stud is the earliest form of the card game stud poker, originating during the American Civil War, but is less commonly played today than many other more popular poker games.
Stud in the context of people usually means an attractive, fit guy. So a very sexy man would be called a stud. "stallion" is a type of horse and can be used in the same way. In this context, it means an attractive man, which derives from the more literal term of a male bull or horse used for breeding.