Everything changed in the years following the end of the Browser Wars I. A number of processes reshaped the web development landscape in a very positive way.
Microsoft won the war, and for about five years (which is more or less forever in Internet time), they stopped adding features to Internet Explorer and JScript. This allowed time for other browsers as well as developers to catch up and even surpass IE's capabilities.
The movement for web standards was embraced by developers and browser vendors alike. Naturally, developers didn't like having to code everything two (or more) times to account for browsers' differences; therefore they liked the idea of having agreed-upon standards that everyone would follow. We're still far from being able to develop in a fully standards-compliant environment, but ideally, this will happen in the future.
Developers and technologies matured and more people started caring about things like usability, progressive enhancement techniques, and accessibility.
In this healthier environment, developers started finding out new and better ways to use the instruments that were already available. After the public release of applications such as Gmail and Google Maps, which were rich on client-side programming, it became clear that JavaScript is a mature, unique in certain ways, and powerful prototypal object-oriented language. The best example of it's rediscovery is the wide adoption of the functionality provided by the XMLHttpRequest object, which was once an IE-only innovation, but was then implemented by most other browsers. XMLHttpRequest allows JavaScript to make HTTP requests and get fresh content from the server in order to update some parts of a page, without a full page reload. Due to the wide use of XMLHttpRequest, a new breed of desktop-like web applications, dubbed AJAX applications, was born.