In contrast to software programs that you install on your own computer and use to do word processing, graphics, and desktop publishing, a web application is one that you operate through a web browser over the Internet. The main program itself resides on a server somewhere while you enter your data (typing words, drawing pictures) at your computer via an online interface using your browser.
Some apps for the desktop or mobile devices (such as the iPad or a smartphone) may have a combination of components that reside on the device but also interact with components on the Web when an Internet connection is present.
"The first mainstream web applications were relatively simple, but the late 90's saw a push toward more complex web applications. Nowadays, millions of Americans use a web application to file their income taxes on the web." — Daniel Nations, former About.com Guide to Web Trends; "What is a Web Application?"