Everyone is supposed to be able to wear a tiara and feel like a princess. (All you boys and men, feel free to substitute a hefty crown, and feeling like a king.)
Apparently, in the past, tiaras were only worn by married women who were royalty.
The reason that this day in particular is International Tiara Day is because it is also Queen Victoria's birthday.
Queen Victoria (Alexandrina Victoria; 24 May 1819 – 22 January 1901) was the monarch of the United Kingdom of Great Britain and Ireland from 20 June 1837 until her death. From 1 May 1876, she used the additional title of Empress of India.