Other educators have commented on the connection between the title of this book and the poem by Burns, but there is also some symbolic meaning behind the title.
Mice are not valued much in society. They are often seen as a nuisance, and mankind often seeks to destroy them. Lennie recognizes that mice aren't just an object of scorn and that they have redeeming qualities, too. He enjoys petting their soft fur and finds them a gentle source of comfort. Lennie appreciates mice as much as he appreciates other innocent creatures, such as rabbits and puppies.
Lennie is much like a mouse in this regard. He has an intellectual disability, and most of mankind doesn't value his existence. He is verbally insulted numerous times in the novel, and even George, who is his closest friend, makes comments like, "If I was a relative of yours I'd shoot myself." Because of his differences, Lennie stands outside the world of acceptance, much like the mice he cares for.
Of Mice and Men, then, comes to illustrate the symbolism of innocence versus evil in the novel. The innocent will find themselves persecuted by those who don't care to find value in their existence. After he accidentally kills Curley's wife, Lennie is killed by the one man he believed he could always count on. The title reflects the way those who are seen as weak are exploited by mankind.