A "Debian Day" has sometimes taken place as part of DebConf, intended to provide talks and workshops about different topics for "normal" interested people, press and companies. It's a day for people which are not deeply involved in Debian, but are curious about it. Sometimes the events have been special ones for only these groups, while sometimes they have been shared with the main DebConf program.
DebianDay is also the name of worldwide one day events around August 16th, the Debian Project Anniversary. In 2013 we intend to merge the DebConf Debian Day back into the general one.
In 2007, Debian Day took place on June 13th, Edinburgh, Scotland, prior to DebConf7.
In 2006, Debian Day took place on the 13th of May in Oaxtepec, Mexico, directly prior to DebConf6, see http://debconf6.debconf.org/debianday/.