Covers are kind of a big deal. Even as ebook sales increase, readers who browse bookstores and libraries are still a large part of the reading/buying audience. Even if the publisher does get the book placed in the new release stands at the front of the chain stores, or faced out in the regular shelves, a passing glance at the cover may be all the chance it gets to make a sale. Covers are also important for attracting the attention of the chain book buyers. They don’t give space or prominent placement to covers they don’t think will sell.
There are a lot of theories, and superstitions, about what makes a good book cover, like the superstition that having non-white characters prominently featured will cause the book to magically fail. This one has been offensive to writers and readers for a long time.
When my fourth novel Wheel of the Infinite came out in 2000, I found out later that the cover artist Donato Giancola had to argue with the publisher to get the cover printed with the protagonist’s real skin color, the way I had described her and he had drawn her. They wanted to show her skin color as gray rather than brown, and some covers were printed that way. I didn’t find out about this until much later, since the authors’ copies I received all had the correct skin tone. (I thought the gray Maskelles I saw occasionally were printing errors.)
When the book came out in paperback, the publisher reversed the cover image, so the white-skinned secondary male character was on the front and Maskelle was on the back. 
Coming up with a good cover is very tricky, because covers have to be both attention-attracting art and also communication, with images that tell readers that they should stop and give this book a second look. But everyone’s taste is different, and covers that attract some readers are guaranteed turn-offs (or pass-by-and-avert-your-eyes) for others. There are also theories about color schemes, that gold or yellow tones draw attention when other colors fade into the bookstore’s background.
One thing I think is important for genre covers is that the art must get across what kind of book it is, whether it’s fantasy, science fiction, mystery, romance, etc. I think it also helps to get across what subgenre the book is. Is it epic fantasy, urban fantasy, sword and sorcery adventure, space opera or hard SF, a cozy mystery or a historical romance, and so on. There’s a belief that having a dragon on a cover automatically sells fantasy novels, and it’s probably true. I don’t think it’s because that many people love dragons; I think it’s because a dragon is a clear signal of fantasy, and it makes fantasy readers pick the book up to see what it’s about.
I’ve seen books that should have done well, with covers that were gorgeous pieces of art, that just didn’t sell because there were no elements that told readers that they were the audience for this book. A fantasy novel that should have been a hit can fail if the cover doesn’t show any hint of magic or strange worlds or creatures, if it has a cover that at a passing glance makes the reader think “men’s adventure” rather than “sword and sorcery.” A science fiction novel might have a beautiful portrait cover of the main character, but nothing to tell the reader that this is science fiction and not mainstream. Also, a beautiful piece of art that doesn’t reduce well to paperback size can do more harm than good.
I don’t think there’s any actual data about how often a cover sells a book versus word of mouth. I do know how often I’ve spotted a cover that made me stop and pick up the book, and I ended up with a new author to read.
