Aunt Clara and the gigantic rabbit do not necessarily symbolize anything. Steinbeck probably intended them to represent the thought processes of a mentally retarded man who is alone, frightened, and guilty. Of Mice and Men relies heavily on dialogue and action, while employing a minimum of authorial exposition and narration. This is because Steinbeck intended to turn his novella into a play, which he did in 1937. In stage plays the exposition is invariably conveyed through dialogue. In the novella, Aunt Clara and the rabbit both give the author an opportunity to write dialogue explaining Lennie's thoughts and feelings while in hiding. It should be noted that although Aunt Clara and the rabbit both are supposedly talking to Lennie, they are tallking with Lennie's voice. In other words, they are only figments of his imagination. He is saying what he thinks they would be saying. The big rabbit is the representation of the rabbits he hoped to have when he and George bought their farm. Steinbeck makes the rabbit exceptionally large because he wants it to be easily visible to an entire theater audience when the story is staged. He could have had Lennie talking to a small rabbit in the story and planned to have him talking to a gigantic stuffed rabbit on the stage--but he seemed to want to make the adaptation as simple as possible, probably because time was of the essence.
The Introduction section in the eNotes Study Guide explains how the stage play was produced in the same year the book was published. Clearly there are many examples in the book of Steinbeck's intention to make the story easily adaptable to the stage. The sets in the novella are as simple as they could possibly be, consisting mainly of a bunkhouse and a barn. In the case of Aunt Clara and the gigantic rabbit, Lennie is all alone and the two hallucinations only exist to allow Lennie to vocalize his feelings of guilt and dread.
If the reader wishes to interpret Aunt Clara and the giant rabbit as symbols, there is, indeed, plausibility for this interpretation. Aunt Clara and the rabbit are the visual voices of his conscience, visuals that in his simplicity Lennie needs in order to conceptualize his thoughts. For, like a child he envisions these main figures in his life as scolding him as she probably has done when he was younger.
And when she [Aunt Clara] spoke, it was in Lennie's voice. "I dol' you...But you don't never take no care. You do bad things....You never give a thought to George...."
Likewise, the giant rabbit underscores Lennie's irresponsibility for which Aunt Clara has chided him and voices Lennie's fears,
"you ain't fit to lick the boots of no rabbit. You'd forget 'em and let 'em go hungry....he's [George's] sick of you. He's gonna beat hell outa you an' then go away an' leave you."
That Aunt Clara and the rabbit use the same dialect as Lennie and are in his "voice" is an indication that they are the products of his conscience and imagination. Moreover, when George comes quietly out of the brush, "the rabbit scuttled back into Lennie's brain." Aunt Clara and the rabbit are symbols of reason and fear, acting as the voices of Lennie's conscience.