'Wobblies' is a slang term for members of the international labour union, the Industrial Workers of the World.
Founded in 1905, the IWW had a membership of around 100,000 at its peak in 1923, and had the power to rally support from 300,000 workers. They believe in the abolition of the wage system and in workplace democracy, with self-management and recallable delegates.
Internal conflict soon split the organisation, but it still exists today, with a membership of some 2,000. Its offices are in Chicago.