Most countries in the world celebrate International Workers Day on May 1. So why does the United States have a completely separate "Labor Day"?
The great irony is that the origins of the May 1 Workers Day were actually in the US. It's important to understand these origins to grasp why it came about that billions of people now celebrate a holiday commemorating events in a country that doesn't honor it.
In 1886, labor unions throughout the industrialized world were making a major push for the 8-hour day*. On May 4, 1886, at a large labor demonstration in Haymarket Square in Chicago, someone threw a bomb and many people were killed, including 7 police. The resulting trial was widely understood to have framed 8 anarchist labor organizers, some of whom were executed.
Over the course of the next few years, international labor organizations adopted May 1-- long a traditional pagan holiday celebrating the arrival of spring-- as a day to commemorate the movement and the events in Chicago, and press for an 8-hour workday. Despite anarchists being the main focus of repression in the aftermath of the Haymarket massacre, there was wide agreement among the left about the importance of memorializing what all Leftists viewed as a major historical moment with huge implications. Despite having excluded anarchists, the International Socialist Congress in Amsterdam in 1904, (part of the "Second International") called on all socialists to stop work on May 1 and to demonstrate to demand the 8-hour day.
After the Bolshevik revolution and the establishment of the USSR, Communists around the world institutionalized May Day as a semi-nationalist (and often militarist) holiday, which persists in all formally Communist and even in formerly Communist countries.
The fervent anti-Communism of the US during the Cold War explains a lot of why we barely know about May Day as a workers' day here, but even between 1887 and 1894, when Labor Day became a US federal holiday, there was much debate about what date it should fall on. Most of the US labor movement favored the May 1 date, which was rapidly becoming a rallying point for workers' movements in Europe and Latin America, but US President Grover Cleveland didn't want any hint of commemoration of the Haymarket affair.
* One quick note about the 8-hour day: this was before the notion of payment by the hour became standard. Workers were expected to show up and work for the entire day-- which could be 10, 12, 14 or even more hours, arbitrarily determined. The goal was that the daily wage would remain the same, but be limited to only working 8 hours. By the time labor legislation was finally passed around this in the US (it wasn't until 1937 that the 40-hour week became law), businesses saw the value in conceiving of labor cost on a per-hour basis, something we've all internalized for generations now.
Sources:
Grant, Jordan. "May Day: America's traditional, radical, complicated holiday". The National Museum of American History
Foner, Philip S. (1986). May Day: A Short History of the International Workers' Holiday, 1886–1986
United States Department of Labor: The History of Labor Day
The Dramas of Haymarket, Chicago Historical Society
EDIT: fixed typos