Those workers in 1886 were demanding the eight-hour day, an old demand. The slogan 8 hours labour, 8 hours recreation, 8 hours rest is attributed to Robert Owen, who could have enunciated it by 1817. Today, two centuries later, most of workers in the world are far from the eight hours work day and, in the last decade, farther each day. But there is a fundamental difference with workers in 19th century: nowadays it seems we don’t mind to work longer for less.
Curiously, USA is one of the few countries in the world where this holiday doesn’t exist although commemorates an affair which happened in Chicago.