What is the significance of Auto-da-Fe in Chapter 6? It does no make sense to me at all.

Yes it was rather senseless but,

"After the earthquake, which had destroyed three-quarters of the city of Lisbon, the wise men of that country could think of no means more effectual to preserve the kingdom from utter ruin than to entertain the people with an auto-da-fe, it having been decided by the University of Coimbra, that the sight of several persons being burned alive in great ceremony is an infallible secret for preventing earthquakes."

They figured a good burning of people alive in costume (Candide had painted with flames reversed and with devils that had neither tails nor claws) would somehow appease the Gods, prevent future earthquakes and entertain people.