Web Designing has to do mainly with design and putting together of static components of a web site, such as CSS, HTML, Graphics and other front end pieces of a website that do not necessary demand coding experience, you do not have to know programming to be a web designer.

Web development on the other hand deals more with building web applications ( programming) that are to offer users dynamic content which is tied to the sites client/server technology, meaning a lot of programming involved. You have to have programming knowledge to be a web developer

web design is simply creating what people see when they visit a web site and like Kobojunkie has pointed out, you don't have to know programming to be a web designer but web development deals with the actual working of your web site usually called the back end because you can't "see" it but you can see the result of ite work.

take for example you can say web design deals with what you can see on the outside of a man but web development deals with how the man thinks (or the design of his soul and spirit) which obviously you can't see