Before 1995, very few people knew what web applications were. Of course, there was an excellent reason for that: very few web applications had been developed up to that point. Websites were becoming popular, but had not developed into the huge market which they comprise today. For discussion purposes, the primary difference between a web site (collection of files in support of a common theme, idea or product) and a web application (web-based data collection and processing tool) is one of complexity. Some popular websites (Amazon and eBay for example) can be seen as a combination of a traditional website and multiple web applications.
Until the advent of the internet, most applications were written to run on local computers and required that the applications be installed for each computer separately (for example, Adobe Photoshop). Or, in those cases where the application was hosted (run from) another computer, often called a server, one still had to install the client application (for example, Microsoft Outlook) on the local computer that would access and run the server-installed application (for example, Microsoft Exchange Server). For this reason, we often hear this traditional type of application referred to as a client-server application (or sometimes simply a desktop application).
Today's web applications take the client-server concept and re-purpose it. We still use clients, but now the client is the browser (usually Internet Explorer or Firefox). We no longer need to install every application on the local machine. Instead, once the browser is installed, we may use it to browse files on our own computer, millions of publicly-available websites and as many web applications as we have access to.
This is not to say that all of the old client-server applications have gone away. Indeed, we've not so much lost the desktop applications as we have built on the foundations which they have provided. One example of this is Microsoft's Outlook Web Access (usually called OWA). This web application allows a user to view his/her email via any standard browser. This means that the user does not need to be logged into his/her computer with Outlook open to work with email. OWA has been around several years, but it has matured to the point where it is almost as full-featured as the standard Microsoft Outlook client.
In other words, web applications are becoming increasingly able to support the types of tasks that we once thought were the realm of the desktop application. If we consider the usefulness of tools such as Google Apps and even ThinkFree, these changes cannot be ignored.