May Day is the international celebration of the labor movement and labor unions. It originated in the 1890's to commemorate the anniversary of the Haymarket Square demonstrations in Chicago. At Haymarket Square, the police violently broke up a labor demonstration for a shorter work day when someone threw a bomb at the police.
May Day is usually observed by demonstrations of party or union strength - like parades, rallies, and other union gatherings. Last May, May Day was a focal point of demonstrations in the Occupy Wall Street movement in NYC, and many unions joined in with a general strike.
Oddly, the United States (the home of the original event that inspired May Day) doesn't officially celebrate May Day. Instead, a similar holiday (Labor Day) is celebrated in September.