Literary fiction is like fiction, but with more literary.
Helpful?
Probably not.
Okay, what it comes down to is that you have your genre fiction, with its focus on pacey plots and relatable characters and mostly, in genre fiction, it is the business of the writer to get out of the way.
As Isaac Asimov put it: “I made up my mind long ago to follow one cardinal rule in all my writing—to be clear. I have given up all thought of writing poetically or symbolically or experimentally, or in any of the other modes that might (if I were good enough) get me a Pulitzer prize."
All that stuff Asimov set aside, that's the literary.
Literary is a twisty bastard. Sometimes it's referring to style. You can have literary and science fiction in the same book (Ursula Le Guin, Doris Lessing), literary and crime (Elmore Leonard), literary and western (Cormac McCarthy).
You also have literary as genre, which is harder to define.
More to come. My brain is tired.
In the meantime, you can always make my life easier and make merry in the comments discussing the definition of literary fiction.
If you want.
Or if you still have no idea what I'm talking about, try the NPR list of literary fiction books:
http://www.npr.org/books/genres/10112/literary-fiction/
For short lit fic online, check out the New York Public Library's guide to online literary magazines:
http://www.nypl.org/weblinks/1249
