Crooks' dream is to work in the ranch George, Lennie, and Candy dream of having. He hopes to just work there on a regular basis as a helping hand, not taking in any pay for his work. He also dreams of making friends with some of the people on the ranch, no matter who it is.
Crooks' dreams affect his relationship with other people because despite him wanting to make friends with others, the other men don't want to be near or even talk to Crooks due to his skin colour. Because of this, he distances himself away from other people and comes off as rude and antisocial, despite him wanting to make friends.
To Crooks, he believes that his dream is no longer worth following, as he requests that he no longer become a part of George, Candy, and Lennie's dream of owning a ranch for themselves after confronting Curley's Wife. He believes that he isn't wanted anywhere anymore and that he should just stick to being alone, and that's what he does. He once again retreats back into his shell and demands that he be left alone, despite his dreams and aspirations.