Google Accelerator decreases the loading time of web pages in your browser (works with IE and Firefox) by prefetching links that you are likely to click on the current web page - thus the linked pages load more quickly.
Update: Google has integrated Accelerator into Chrome and is no longer available as a separate download. It's called Google Instant and here's a guide on how to add Google Instant support to your website.
I have been using the software for over 40 hours now and the performance statistics say that the software helped me save 1.1 hours of web browsing. That means it would have taken 1.1 hours more for the web pages to download had I not been using the Google Accelerator software.
It's difficult to guess how Google decides what web pages to load in advance but my experience has been that if your hover the mouse over a hyperlink for few seconds, Google assumes that you are likely to visit that page and it will prefetch it. Google Accelerator also downloads the top search results on Google.com which is quite logical.
While Google stats say that web pages load faster on my machine after installing their accelerator, the gain is very difficult to visualize - I could not find a single website that loaded faster than before. [Am on a 256 kbps connection]. Maybe the delta is few milliseconds per web page and it slowly adds up.
If you maintain a website or a blog, you can easily specify links that you want the software to prefetch - simply add the following snippet somewhere in your page's HTML source code: <link rel="prefetch" href="URL">. This syntax is also supported on Mozilla Firefox browsers.