Also commonly known as bibs or vests, a pinny refers to the colorful practice shirts that players wear when a drill or activity calls for the players to be broken up into teams. The word pinny comes from pinafore which is:
A pinafore is a full apron with two holes for the arms that is tied or buttoned in the back, usually below the neck. Pinafores have complete front shaped over shoulder while aprons usually have no or smaller bibs. A child's garment to wear at school or for play would be a pinafore.
The pinafore was a type of apron that was pinned over the dress and easily removed for washing. Buttons were frequently damaged with lye cleaning products, which was one reason why dresses were not laundered very often. The pinafore had no buttons, was simply "pinned on the front" which led to the term "pinafore."
So in essence, it was a sleeveless garment meant to be worn over a dress by children when they played to protect the dress as the pinafore was easier to launder.