Why is it so important to Antigone to have her brother buried? What religious belief is being displayed?

In order for the spirit to be "at rest," a burial must occur. The money had to be placed on the body in order to carry the soul across the River Styx to the Underworld. If the ritual was not performed, then his spirit would haunt this world for eternity.

The religious belief that is being displayed is that spiritual law was more important than civil law. The gods decree that the burial ritual must take place. Creon was placing himself above the gods in ordering no burial to take place.