In the US Labor Day has always been associated with labor unions, who created the idea for the holiday and pushed for its acceptance. Our first in the US didn't come until 1882, and then only in NYC. But over the next 2 decades it spread to whole states, until by the early part of the 20th Century the entire US was celebrating it.
It served to honor all workers, those in unions in particular, and to provide a platform, especially through parades, for the union agenda. This included a shorter work week, better & safer working conditions, minimum wage, and benefits packages.
In the US today it means a long weekend, family picnics & cookouts, and some vague connection with people who work. Some of whom wish it didn't exist, because it's not a paid holiday for them and they lose a day's pay.