Being short-handed means not having the necessary number of people to help with something. If six friends promise to supervise your brother's birthday party with you but only two show up, you'll be seriously short-handed!
Short-handed was first used in the 17th century to refer to a workplace that has an insufficient number of "hands," or workers. You can use it whenever you're in a situation where fewer people than normal show up or help out: "We were short-handed at the restaurant last night so I had to cook the burgers, deliver them to customers, and help wash the dishes!"