Symbolism, Imagery, Allegory
Having your own land and being your own boss are the cornerstones of the American Dream. And the cornerstone of land is a barn. And the cornerstone of a barn is…a cornerstone.
Basically, farms and barns are great symbols for the American Dream because they enable you to live off the sweat of your brow. Remember George and Lennie's dream from Of Mice and Men? It's to get a little house, a couple of acres, a cow, some pigs and rabbits, and to "live off the fatta the lan.'"
In some ways, Tom's story is kind of a way-less-depressing, coming-of-age version of Of Mice and Men, also using the barn/farm symbol as the emblem of the American Dream. Tom's ultimate goal is to have a farm that turns enough profit to support his family and to show the world that he's made something of himself. The first step to having a good farm is having a good barn, because that is where farmers house their animals and equipment. He's really got this worked out.
While Tom is working on getting the Breen barn, the barn represents his hopes and dreams. Once he owns it, it continues to symbolize his aspirations for the future, but it also symbolizes the hard work he's already put in and the success he's attained.