1. Reviews sell books figuratively. In the figurative sense, readers tend to think that a book with more reviews is more popular, and therefore has more merit and is worth buying. Readers also read reviews to determine whether they'll like a book, because they know that the stuff on the back jacket flap is basically a commercial, and commercials lie.
2. Reviews also sell books literally. Online bookstores and marketing sites have algorithms that determine which books will be recommended to their patrons. Reviews figure prominently in determining this algorithm. So to get recommendations or to purchase advertising I need reviews.
3. Anyone can write a review. Some readers think their opinion doesn't matter or that reviews are best left up to professional critics. Actually, in the social media age, the opinions of average readers are much more important than those of critics. A book's overall rating is based on an aggregate of all the reviews it's received. So instead of Roger Ebert saying "three stars" and that being the end of the matter, we're relying on hundreds, possibly thousands of people just like you to say what you feel, and then averaging out the results.
4. A review does not have to be hard or long. As I mentioned in point 3 above, leaving reviews leads to an aggregate score, so writers need as many reviews as possible for buyers to accurately gauge a book's quality. Not every review is going to be 1000 words, or some kind of in-depth analysis. Amazon used to have a twenty-word limit on reviews, but not even that is true anymore. You can literally write "I liked it" or "I hated it" and that's enough.
5. A subjectively "bad" review is good for the author. One reason readers cite for not leaving reviews is that if they didn't like the book and they don't want to hurt the author's feelings (or, worse, invite the author's wrath.) While we may weep over a one-star privately, every author worth his or her salt knows that bad reviews drive those algorithms I mentioned in point 2 above, and they also drive readers the way I mentioned in point 1 above. The classic example would be leaving a one-star review and saying "every God-fearing conservative will shun this book" will drive progressive readers to actually buy the book. And while I can't promise anything for every idiot out there, I can promise for myself that no review you leave will make me hunt you down, online or in person, or in any way treat you unkindly.
6. You don't have to buy a book on Amazon to review it on Amazon. There are several sites where you can leave book reviews: Goodreads, Barnes and Nobles, Booklikes, etc. But let's be blunt: Amazon is where most book sales are made, and Amazon is where reviews do the most good. Some readers don't like to leave an Amazon review, though, if they bought the book at a bookstore or on another site. Well, there is actually no limitation on doing so. Amazon has "verified" reviews meaning they know you bought the book through them, but they also allow anyone with an account to leave a review on anything. Again, because the goal is to aggregate scores, Amazon is hoping that wherever you bought the book, you will nevertheless leave your opinion on their site. For good or for ill, Amazon is the review site of record these days.
7. Leaving a review is easy. Some readers complain that leaving a review is too hard, or takes up too much time, or is hard to remember to do. Well, I can't speak for anyone else, but I just made you twelve little easy buttons. Click on the cover below of any of my books that you've read and you can leave a review just like that, lickety split. And I hope you will. :) Thanks, everybody!