In the fairy tale, the baker must expiate his father’s sins by bringing the witch three ingredients for a magic potion: a cow, a cape and a slipper. Expiate means to make amends or atone for a wrong you or someone else has committed.
After the incident on the hill, a mortified Jill expiated her guilt by buying Jack a brand new crown. The shiny new crown served as compensation, or expiation, for the broken one. That it cost her so dearly made the expiatory gesture especially meaningful to poor Jack.