Games are a huge part of childhood. Some teach valuable skills that are put into use in the world of grown ups, like chess that assists the development of strategy and problem-solving skills.
In this particular image, the young girl is playing an ancient street game of knucklebones or astralagoii. It is a game that is similar to dice or jacks and can be played in many different ways. Boys and girls would play this game together and are often depicted this way.
Because this is a Roman copy of a Hellenistic statue, she is wearing a Greek style chiton outfit that clings to the figure, fastened at the shoulders and is tied at the waist with a belt. It is never quite clear why clothing is shown falling off of the body of young girls. She is not playing a game that requires great movement, although as children tend to focus on the action at hand, it may just be a carelessly fallen sleeve.
Her hair is represented in tight curls or cornrows, often called melon style. This was a very popular look for girls, owing either to their very curly hair or it being an easy way to render it in marble.