To the uninitiated, Boost is a module for Drupal which has the potential to make your Drupal-based website run many times faster than it's currently running. Boost basically converts pages on a Drupal site into static html files, and allows your website to direct anonymous (non-logged-in) users to the cached html pages.
Doing so speeds your site up quite a bit, because instead of your web server having to run some PHP scripts and connect to your website's database, the server can simply send the complete html file, which requires no extra processor cycles or memory to compile. If your website has a lot of anonymous traffic, the potential speedup is very large. Instead of serving hundreds of users per minute, you could serve thousands.