What did the rabbits symbolize?

For the most part, the rabbits symbolize Lennie's dream of the good life. Lennie yearns for nothing more than to live on a farm with George and tend rabbits. Lennie is a gentle soul with a fondness for small creatures, even though he is a physically large man who does not understand his own strength. In a sense, fragile and innocent little rabbits appeal to Lennie, likely because he sees something in them that reminds him of himself. Throughout the story, Lennie asks George to tell him about how he will be in charge of the rabbits once they have their farm. It is his dream and what keeps him motivated.
In another sense, the rabbits represent futility. When you think about it, there is no way that Lennie would be good at taking care of rabbits. Despite his innocent intentions, his clumsiness and strength cause him to destroy almost everything that he touches. He crushes the mouse he keeps in his pocket. The same thing happens to the puppy he was taking care of. Indeed, he even accidentally kills Curly's wife in a similar manner. There is no way he would have been able to take care of rabbits without doing the same. So the dream of tending rabbits remains just that, a dream, and one that tragically is never to be achieved.

In Of Mice and Men by John Steinbeck, George and Lennie are two migrant farm workers during the Great Depression in the Salinas River Valley of California. Unlike the majority of migrants, George and Lennie travel together, mostly because the latter has an undisclosed mental impairment, a fact that makes George feel responsible for looking after Lennie to keep him out of trouble. Part of what binds them as friends, however, is their shared vision of the American dream: the pair have extensively discussed the small piece of land they hope to purchase and live off of the “fatta’ the lan,’” as Lennie says.
The most important part of this dream for Lennie is his wish to have rabbits, for which he would be responsible. In the very first section of the text, Lennie insists that George recite the details of this fantasy, specifically to tell Lennie about the rabbits of varied colors. Lennie is interested in rabbits because he loves to pet soft animals as a means of comfort, and his desire to tend the rabbits is the driving reason behind Lennie’s actions throughout the novella.
When Lennie accidentally kills the pup in the barn, he is angry with himself because he worries that George will no longer allow him to tend rabbits in the future. This frustration and stress at the loss of what he wants most is also what drives him to accidentally murder Curley’s wife.
Each of these details about the rabbits suggests that Lennie views the creatures as his only hope for happiness. When he fears that he has lost hope permanently, Lennie desperately tries to recover that hope by concealing his crimes. Of course, Lennie is unsuccessful in recovering his lost hope.
In the last section of the novella, George makes the tough choice to shoot Lennie; otherwise, the enraged Curley and his posse would likely make Lennie suffer. In order to make Lennie’s death a peaceful one, George again tells the story of their dream, and Lennie mentions the rabbits in his last breath. This further illustrates that these rabbits represent hope in this narrative. Lennie dies still hopeful that the future will be better than the present.

In Of Mice and Men, the rabbits are a feature of George and Lennie's dream to own their own ranch and live off the land. As such, the rabbits represent economic freedom and their hope for a better life together.
For Lennie specifically, the rabbits also function as a symbol of happiness. Notice how he often he talks about tending to the rabbits on his dream ranch. For him, the rabbits are a symbol of comfort and pleasure.
At the end of the novel, just before Lennie's death, he has a vision of a giant rabbit. It says to him that he is not "fit to lick the boots of no rabbit" and that George will never let him tend any rabbits because of the bad things he has done. 
This vision is significant because it suggests that George and Lennie's dreams will never come true. No matter how hard they try, they will never be able to escape the harsh realities of their existence and buy their own piece of land.