Models, prediction, statistics, the Internet and the human brain
This new service from Google is useful when you have to write in English, or any other language.
The best way to understand it is to use it. It is not a spell checker, it is a prediction engine. Play with it, and you'll realize how helpful it can be.
The technology behind it is called statistical machine learning. The approach is not to hire an army of linguistics and devise all the rules of language (if it were possible!). Rather, the approach is to analyze a huge amount of information on the Net and extract statistics. So, to simplify, you can calculate the likelihood of one word coming after another.
This is the first step of course, because it would be great to add a context, or better yet the likelihood given the phrase, context, etc.
If you want know more about the background, here is an interview with Peter Norvig from Google.