Starch retrogradation is the process in which cooked starch molecules (amylose and amylopectin) slowly realign and form more ordered, crystalline structures as they cool and sit. In baked goods, this can cause the texture to become firmer, drier, or powdery over time.
Amylose is a mostly short, linear molecule, so it can realign relatively easily. Amylopectin is much larger and highly branched, which makes this realignment more difficult and thus, retrogradation occurs more slowly.
Retrogradation doesn't affect just baked goods - it also affects starch-thickened gels, such as puddings and pastry creams. As the starch molecules realign, they can squeeze water out of the gel, causing liquid to collect on the surface. This water separation is called syneresis.