"Q. What kind of flower is that on the cover, and what does it mean?
A. That is a ruffled tulip. As for the meaning... If you've read the Twilight FAQ, you know that the apple cover had a lot of meaning for me, and I was an active part of the covering process. However, that experience is more the exception than the rule in the publishing world. Something to keep in mind if you intend to embark on a career as a writer: lots of things you might expect to be under your control are not. Covers, for example. Those are mostly up to the publisher and the marketing and sales departments. So I don't know what the tulip means—I didn't have anything to do with this one."
You can find it under Twilight Series > New Moon > FAQ.
Hope I helped :P
Lot's of people have different opinions on this, but I believe that the flower represents Bella's heart. Why? Because I think that it's red because she's hurt inside, and the white represents a little bit of hope/love that's still there. However there's a petal dropping off because she feels as if she's falling apart. But, that's just my view, most people's are different.
There are sites that say the flower has absolutely no meaning seeing as Stephanie Meyer did not choose the cover for New Moon.
Then there are some sites that say the ruffled tulip represents a beautiful butterfly coming into view.
I'm not sure which one is true, but that's all I could find.
I believe that the this flower fades, and it represents as she feels Bella when Edward goes away, but for it me represents sinceBella's heart is in this book, the white thing represents the cold (is Edward) and the red thing is the heat in this case he would be Jacob.