Listening to your web content rather than looking at it can be an "eye-opening" experience (pardon the pun) that takes sighted users out of their normal comfort zone. It gives sighted users a chance to evaluate their content from an entirely different perspective: from the perspective of a blind person. A lot of times you'll end up finding mistakes that would have been hard to catch visually. For example, spelling mistakes become very obvious when you hear words mispronounced by the screen reader. Screen readers are also very good for checking the accuracy and quality of image alternative text. Screen readers can also help you identify problems with reading order, table markup, form elements, and many other aspects of accessibility.