AJAX has allowed for better and more intuitive web applications, web mashups allow for unique and interesting new combinations of applications, and the social web has put us into the web as active participants, but it is cloud computing that is taking the web to the next level by turning it into a platform.
We already have many great examples of cloud computing from Google Docs, a suite of free online office applications that includes a word processor and spreadsheet, to Wolfram|Alpha, a "decision engine" that can perform sophisticated calculations. Many of us use cloud computing without even thinking about it. For example, the iPhone app Shazam can recognize what song is playing on the radio, but it isn't the iPhone that is doing the heavy lifting. The app is simply transmitting the information to 'the cloud' (Shazam servers on the Internet) to break down the music and find the song.
And we are really just at the tip of the iceburg. Google is leveraging its Chrome browser and turning it into an operating system in order to create cheap "terminals" capable of access the web and running sophisticated applications through the rise of cloud computing. And HTML 5, the new web standard currently being worked on, will allow for even more sophisticated applications.
In the end, this means we won't be tied to a specific operating system like Microsoft Windows and we won't need an expensive computer. Even if we need to do some heavy lifting, we can rely on the Internet to power the applications while we access it through a relatively cheap 'terminal' of a computer.