How does an individual use a personal computer? Barring edge cases, like using niche applications for business purposes, we can generalize it to editing and storing documents, pictures, music and other files, managing appointments and tasks, and doing a whole bunch of things on Internet like checking emails, social networking, surfing, getting news and so on. These uses of a personal computer makes it such a formidable force, both at home and work. The base of a personal computer is an operating system (like Windows, Linux, Mac OS) making it the platform of the computing world.
Now consider a web browser such as the Internet Explorer or Firefox. What can a web browser do? It can connect a personal computer to the grid of servers out there somewhere in the cloud. All you need is this browser and an Internet connection. If this grid of servers can store your documents, pictures, music and so on, and the browser can provide you with tools to create and edit these items, manage your calendar and let you use the Internet as usual, your need of owning a powerful computer and cutting edge operating system diminishes significantly. The platform now changes from a personal computer to an Internet browser running on this personal computer.
When the required platform changes from an operating system to a web browser, what happens? You stop looking for the latest operating system for your personal computer and start marching towards the latest and most efficient web browser. No doubt you will still need a personal computer, but you might not need to update it every three years to stay in sync with the doubling computing power. This challenge posed by a web browser to the operation system is a case of challenging an existing platform not with a better platform, but with a different platform.