In Ancient Roman times, the year ended with February and the new year began on March 1, which was also the first day of spring (primo vere). March 8 was one of the first of the springtime festae, a day sacred to Ariadne, whom Thesius had abandoned on the Island of Naxos after promising to marry her if she helped him slay her father's pet Minotaur. Seduced and abandoned, she was a prototype for ancient Mediterranean womanhood.
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. Other yellow flowers also carry the sentiment, if you Mimosa is out of reach.