
For the subject see Ovid, 'Metamorphoses' (6). Apollo defeated the satyr Marsyas in a musical competition; as a punishment for failure, Apollo flayed him.
The picture was originally above the door of the Stanza di Apollo in Villa Aldobrandini, hence its horizontal format.
While the landscape and the main figure group are convincingly by Domenichino himself, it would seem he left the painting of the right side to an assistant. Six drawings for the composition (Windsor, Royal Collection) include a chalk study of the landscape without the figures.