This term, which looks on first glance looks like it could be a type of fancy European pastry, can essentially have two meanings, neither one of them dealing with dough. First, it can be used to mean a combination or hodge-podge of artistic work that comes together to make one all-encompassing composition. The second meaning is that of an artistic endeavor that imitates the style of work that has come before it. It is this latter definition that is most commonly seen in the design world.
Example: Every time Barbara drove around the new housing developments in her neighborhood she flinched at the pastiche. Once a peaceful, wooded, suburban retreat comprised of 1930s bungalows, the area was quickly being overtaken with ridiculously designed, cheaply executed NeoClassical McMansions.