Within general art, this usually refers to an often light-hearted imitation of another artist's style. More broadly, this can refer to art which uses the style or pieces from an earlier production as central pieces. This can be poor imitation (like much of fan fiction and fantasy literature), but can also be innovative, such as the film Moulin Rouge which used verbatim popular songs in an unusual musical.

References:

• Narrativism: Story Now
• Pastiche in Roleplaying