The phrase Bonfire of the Vanities refers to an event that took place in Florence, Italy on February 7th, 1497.

It was near the beginning of the Renaissance when a Dominican monk named Girolamo Savonarola, who some call ultra-conservative, others fanatical, preached to the population of Florence against the decadence of the times and pointed to the wealth of possessions held by the Florentines as a sin of vanity.

Savonarola told the people that they must (or more likely forced them to) destroy the possessions that had distracted them from God and reject the popular decadence that was emerging.

Savonarola persuaded or coerced hundreds of Florentines into bringing their wealthy possession to the Piazza della Signoria during the Shrove Tuesday festival of 1497, where they were burned on a great pyre. Some accounts say there were many bonfires while others say it was a single fire, 15 stories high. Books, paintings, mirrors, fine clothes and musical instruments were among the possessions destroyed.

Today there is a plaque set in the ground in front of the fountain of the piazza to commemorate the event.


Sources:
http://www.floria-publications.com/italy/italian_culture/the_bonfire_of_the_vanities.html
http://en.wikipedia.org/wiki/Bonfire_Of_The_Vanities
http://en.wikipedia.org/wiki/Florence,_Italy
http://www.thereareplaces.com/Guidebook/pdest/itflonpts.htm
http://www.italyheaven.co.uk/tuscany/florence/history.html
http://www.guide2florence.co.uk/

Notes:
Obviously, I've left out virtually all of the history of Girolamo Savonarola, since that's covered in a node of the same name.

The novel by Tom Wolfe is entitled The Bonfire of the Vanities, as is the 1990 movie by Brian De Palma.