An application that is implemented inside a Web Browser with most functionality implemented on the server side (Web Server or Application Server).
Web applications are often implemented with J2ee (jsp, servlets,...) CGI, Allaire Cold Fusion, ASP, and so on.
Other definition that was here before:
The module of the overall application that handles a user session, application flow, Web Page requests, navigation. This is as opposed to the Stored Procedures, EJBServer, and JSP Servlets although the JSP Servlets are part of the Web Application technically, in our development environment we keep JSP Servlets separate.
See virtualschool.edu 
[Broken Link] for articles and software for WAP, which has
proven far more productive than perl and/or JSP for my needs at least. Described
in the May 2001 Dr. Dobbs' Journal. -- Brad Cox
There are some applicaltions that run completely locally but are designed like Web Application's. An example is Yandex Personal Search http://desktop.yandex.ru/how.xml desktop.yandex.ru - an utility for local search of files, that runs residentally as a local HTTP server and is accessed by an HTTP link - so it looks like a popular Russian web search engine. Less precise example is Diff Daff http://www.cyberpromote.de/software/diffdaff.htm www.cyberpromote.de - a local file compare tool that produces output in an HTML page.
I thought a Web Application was precisely the opposite of the definition given at the top of this page: an application with most of its code implemented client side in Java Script and using HTML/CSS for its UI, not requiring a server to be installed locally.. A web app should not require be able to perform its function with no internet connection, only requiring net access for data or code updates.
Also see Web Application Design, Web Applications And Xp, Web Form Methodologies, Web Application Problem Domain
See original on c2.com