People in different parts of the world spell different words differently, and the word labo(u)r is no exception. With this word though, the associated meaning is also different and so is the day it is celebrated on in America and in the rest of the world.
Quoting from this article on Wikipedia,
The celebration of Labour Day has its origins in the eight hour day movement, which advocated eight hours for work, eight hours for recreation, and eight hours for rest. On 21 April 1856 Stonemasons and building workers on building sites around Melbourne, Australia, stopped work and marched from the University of Melbourne to Parliament House to achieve an eight hour day. Their direct action protest was a success, and they are noted as the first organized workers in the world to achieve an eight hour day with no loss of pay, which subsequently inspired the celebration of Labour Day and May Day.Remember though, this is the Labour with a 'U' - same as AUstralia. Even then, different parts of Australia celebrate the day on different days of the year and only Queensland and the Northern Territory celebrate it on the first Monday of May (like the rest of the world). Other parts of Australia celebrate Labour Day in either March or October.
As for the American Labor day, from this article in Wikipedia,
Labor Day is a United States federal holiday that takes place on the first Monday in September. The holiday began in 1882, originating from a desire by the Central Labor Union to create a day off for the "working man". It is still celebrated mainly as a day of rest and marks the symbolic end of summer for many. Labor Day became a federal holiday by Act of Congress in 1894.Happy Labor day to all in America! Happy forthcoming labor day to people who celebrate it later in the year. An 8 hour work day was a good idea, not in France anymore though. To all the workaholics out there, don't substitute work for other activities that help maintain a balance in your life.