rug backing is a kind of rubbery textured material that will keep the rug from slipping on a smooth floor. you can find it at wal-mart or similar stores in pre-sized rolls and then cut them to size. it usually comes in kind of an ecru or light tan color, so maybe it won't detract too much from your colors or pattern.

oops, double posted on accident.

I have also purchased this pattern...I know that I need a backing for it, but didn't want the backing to show through to the front.
I have not yet made the rug, but did have a few thoughts on how to tackle this problem.

If you use the "puffy" rug backing (reminds me of placemats and shelf liner that I have seen), you could cut it to fit the rug, and then cut out the middle section where the roses are. You could even go so far as to tack it in place on the underside of the rug with a needle and thread or even yarn.
Another thought that I had was to try using the "sticky" rug backing. It comes in strips or on a roll, almost like tape. It actually reminds me of drywall tape that it used to cover the seams before covering with joint compound.
Anyway, you could cut a few strips the length of the rug. I don't know how well it will adhere to the yarn though, as I have not yet even begun to make mine.
Hope this helps!

P.S. Please let us know your thoughts on the rug (did it work up nicely? Any problems? Should it use a different yarn?), and what you decided to go with for a backing.
Thanks!

hooksx3 and elizabethann - Thank you so much for your very helpful advice.

elizabethann - As for the pattern; joining the 3 rings in the center didn't work up well for me. The pattern said "holding this ring and the next ring together tog, dc in next dc through both thicknesses, ch2." It seemed fine joining Ring 1 to Ring 2 and then Ring 2 to Ring 3, but when joining Ring 3 to Ring 2, the pattern doesn't indicate how many stitches to skip on Ring 2 when joining it to Ring 3 with the dc. So, I mated stitch for stitch Ring 3 against Ring 2 and continued with the pattern. Doing the same when joining Ring 2 to Ring 1. The result was Ring 2 and Ring 3 overlapped in the center and Ring 1 and Ring 2 edges butted up against each other evenly, AND I couldn't finish the stitches around Ring 1 to complete the row because there were too many stitches left on Ring 1 to join to the Row's beginning chain. I ripped it out 3 times getting the same result before somehow managing to get close enough to the ending chain to join the row closed, and achieving the (42 ch sps) required. Deciding to continue on, I then found when working the chain stitch (rows 5-7), The pattern doesn't indicate how many chain spaces you should have. So when completing Row 8, I ended up with (193 dc) instead of (189 dc). A bit frustrated, it has been sitting for a week. I can't decide whether to skip the surprise and inlist the advanced crochet skills of my mom, or go buy her a birthday present and try and figure out the pattern, then give the rug to her for Christmas. My other thought is to crochet a pillow cover, and attached to it the roses and leaves I completed from this rug pattern.