The phrase "biggest union" refers to the largest and most influential organization formed by a group of workers to represent their interests and negotiate with employers on issues such as wages, working conditions, and benefits. Full definition
Imagine, a great big union that is going to take care of us all! (remonline.com)
Last July 2012, the leaders of the two biggest unions in Spain had a secret meeting with Angela Merkel in Berlin, only informing the Spanish Prime Minister afterwards on its content. (blog.politics.ox.ac.uk)