Slackbridge, a union organizer, makes a speech to the Coketown workers, urging them to join the union he represents. This would be a huge deal, since unionized workers would be able to go on strike against the factory owners. (Check out the "Websites" section for some info about the Preston Strike – a real life factory strike that Dickens went to see and wrote about while working on this novel.)
Slackbridge is a wordy blowhard, but his main point about sticking it to the man for the bad conditions and low pay plays well to the crowd.
After a general call to action, Slackbridge singles out Stephen as the only man among them who refuses to join. The crowd is at first angry, then calms down when Stephen starts to speak to them.
Stephen asks to be excused from joining. He supports the workers, but feels like it's wrong to unionize, and also has some personal reason that he won't share for staying out of it. He says that he knows that they will now completely stop having anything to do with him because of this.
The other workers ask him to reconsider, but he just leaves.
From then on, none of the workers acknowledges his presence in any way – and they even cross to the other side of the street if they see him coming. It is an awful, overwhelming experience. Stephen makes it even harder on himself by also avoiding Rachael. Even though the women aren't required to avoid him, he worries that if she is seen with him, she will have problems with her fellow workers.
One night after work, Bitzer asks Stephen to come to Bounderby's house.