ComputerGames played in a web browser, using a plug-in to host a virtual machine run-time environment.
The most common examples now (2003) would be Java and Flash. However it is possible to use simple scripting languages, although this usually precludes smooth animations, which restricts the kinds of games possible.
Javascript has been successfully used to create arcade style webgames. Javascript and dHTML allow designers to manipulate elements on the browser screen, which can be used to create sprite based animation found in many games. Pre 2000, javascript design often resulted in slow games. However as computers have become faster and browsers more sophisticated (using DOM2) javascript games are largely indistinguishable from Java games.
WebGames are distinct from OnlineGames, a larger category of which they are a part.