Carlson asks Slim about his dog's puppies. He is thinking that Candy could have one of these pups because Candy's old dog is smelly, old and suffering. When Carlson asks this, George and Lennie overhear this conversation and George promises to ask Slim if Lennie could have one of the puppies, a brown and white one. It affects George and Lennie because George knows that Lennie likes to pet soft things, so he wants to please his friend and give him this puppy that will make Lennie happy. Unfortunately, George doesn't realize that this is the next step in Lennie's downfall. Although George is perceptive, he doesn't know that Lennie will kill the pup by petting it too hard, and then killing Curley's wife by "petting" her hair too hard. Therefore, Carlson talking to Slim about the pups begins the progression of Lennie's death.
In Chapter 2 Carlson reveals that he wants Candy to kill his old dog. This is an emotional scene in which Candy argues that he can not possibly kill his dog because he's "had 'im too long". Carlson is brutal with Candy and argues that the dog is old and smelly and can't even eat solid food anymore. Eventually, with the encouragement of Slim, Candy agrees to let Carlson shoot his dog.
This scene affects George and Lennie because it solidifies their relationship with Candy. George feels bad for him and later in the novel, George and Lennie include Candy in their American Dream to get a ranch of their own.