A Web app is an application that runs on your browser. A good example is gmail. Unlike a website a web app is about user interaction; as a matter of fact, most popular products today are built as web applications. Software as a Service is a business model most often used in enterprise space, although there are numerous consumer products operating as for example the highly successful Silicon Valley startup Dropbox.
SaaS is practically a subscription business model, where users pay recurring fees for ability to use your product. It can be a highly profitable, predictable and secure business model… if executed the right way.