Before the Second World War, Women's Day had been celebrated on different days in early March in several Italian cities. In 1945, the Union of Italian Women decided to hold all celebrations and commemorations on March 8. However appropriate it would have been, they didn't have Ariadne in mind. In fact they were memorializing two events outside of Italy: a March 8, 1857, strike by women garment workers in New York, which led to the formation two years later of the first women's union in the United States, and a strike by Russian women calling for "bread and peace" on March 8, 1917 (February 23 on the old Russian calendar but March 8 in the rest of the world.)
Authorities don't agree how or why, but the custom started in Italy -- some sources say in Rome in 1946 -- of men giving their wives, mothers, daughters, and other women friends sprigs of bright yellow Mimosa flowers on March 8. Women have since also started to give Mimosa to each other. The flowers are intended as a sign of respect for the women and also an expression of solidarity with the women in their support for oppressed women worldwide. This mild year some Mimosa trees in Rome were already in bloom at the end of January, so there may not be much left by March 8. Other yellow flowers also carry the sentiment, if you can't find Mimosa.
It's possible to send Mimosa or other yellow flowers by wire to more distant women, and there are, inevitably, Internet sites where you can send "virtual mimosa":
Virtual mimosa site: http://www.amando.it/cartoline/compose.php?imageid=281
Information on the Italian origin of giving Mimosa can be found (in Italian) at: http://www.comune.modena.it/~pdangelo/Festadonna/
P.S.: 1. There was, for a time, some resistance to the custom of giving women Mimosa, because it was heavily supported by Italian Socialists (and was exported by them to other countries -- Russia and Japan in particular), but that appears to have evaporated over the years. Last year, an Italian woman friend objected that the custom was sexist -- women should reciprocate by also giving Mimosa to men.
P.S.: 2. Mimosa (acacia dealbata) was introduced to Europe from Australia in 1820 and spread rapidly. Pretty as it is, Mimosa is not a particularly good neighbor to other plants. It is invasive, propagating freely from seed and also by sprouting new shoots from a dense spreading root structure, and it's also allelopathic -- chemicals that are washed down by rain suppress blooming of nearby plants. Since Mimosa plants bloom before grapes, for example, they should not be planted near vineyards. Mimosa is cultivated for its flowers (for cut flowers and honey production) and for essential oils (for use in perfumes and cosmetics). It's dense growth and spines make it a good hedge plant, and its wood is sometimes used in bent-wood furniture. Both of the Internet sites listed above have pictures and illustrations of what Mimosa looks like.