Lennie is a man who, in many ways, still has the mind of a child. He struggles to process the world around him, and his cognitive challenges make him an easy target for verbal abuse. However, Lennie is also a large man with a great deal of physical strength, and this ultimately proves to be an unfortunate combination of traits.
Lennie tends to fixate on objects, and small, furry objects in particular seem to bring him great comfort. He loves bunnies, puppies, and even mice. When George finds that Lennie has been keeping a dead mouse in his pocket, Lennie explains,
I wasn't doin' nothing bad with it, George. Jus' strokin' it.
On the surface, the mouse is simply another small, fuzzy creature that gives Lennie a sense of peace and quiet joy. Yet Lennie is also unable to accurately gauge the pressure and strength he's exerting on these small animals and has a history of inadvertently harming them. Lennie's rough behavior with the mice ultimately foreshadows his treatment of the puppy and, later, the tragic incident with Curley's wife.
On a symbolic level, there are similarities between Lennie and the mice he loves so much. As a species, mice are generally scorned by mankind and viewed with contempt, just as most people dismiss or make fun of Lennie. The circumstances of Lennie's tragic death suggest that his life was never really valued by anyone other than George—much like the mice he loves to pet.