That is a question I frequently get asked, and it's a hard one to answer. When I say that I have a contemporary craft gallery people mostly ignore the word gallery and assume I have a store that sells scrap booking and knitting supplies. Don't get me wrong, I have nothing against scrap bookers and knitters (some of them are my best friends), but it's not what I do. I've searched the internet for a definition of contemporary crafts. Most of what I found was extremely limited or so esoteric as to not make any sense. Now, I'm not promising to make any sense, but I'll do my best.
The things I look for in contemporary crafts and craft artists are:
1. Utility---Not everything that is contemporary crafts is functional, but most can trace its roots back to something that was (or still is) a part of everyday life. A perfect example of this would be blown glass. This beautiful, hand blown, etched vase is in no way utilitarian. It was never meant to be anything other than beautiful and decorative. Yet, you can trace the roots of glassblowing back thousands of years in the making of drinking glasses, bowls, windows, and more. 
2. Vision---The ability to see something in a common object that wasn't readily visible to others. When you see a piece of scrap wood, do you see fuel for a fireplace or do you see the figure of an angel with something to say? When you see an old muffler, do you see something to throw away or do you see the body of a dog?
3. Mark of the Hand---Contemporary craft should show that it was made by a person, with skill and care. Even when something is made with the most cutting edge machinery, it should still show something of the artist in it.
My description of contemporary craft is by no means definitive. Some people will disagree with it totally. Some will say it is too broad. Some will say it's too vague. I challenge them to come up with their own definition (it's not as easy as you think.) These are just the guidelines I use for choosing work for my gallery. After that, it just comes down to what I love. And even then I've been known to throw the rules out the window for something I truly love!
I'd love to hear your definition of Contemporary Fine Crafts.