What if you or your webmaster made an erroneous change on your website, and you didn't make a backup of the code that you changed, and it took you over a day or a week to realize your mistake, which would mean that your website service provider (aka host) also would not have a backup, because they only keep backups of a day or a few days prior.
As a last ditch effort, you hope that www.archive.org took a snapshot of your website from long ago, and archived it. This archiving system may go the step farther by saving the code so that you can "View Source Code," copy it, and put it back into your current site. Archive.org may provide your website to you from 5 years ago, 2, or even 1 if you're lucky.
Archive.org can also be used to track the visual and functional changes that your competitors have made, or that a website you admire has made. You can watch over time to see what they kept, deleted, improved upon, and see if you might want to make simular adjustments to your design and functionality.
According to Wikipedia, Archive.org is known as The Wayback Machine and "...is a digital time capsule created by the Internet Archive. It is maintained with content from Alexa Internet. This service allows users to see archived versions of web pages across time—what the Archive calls a 'three dimensional index.'" The name is a reference to a segment from The Rocky and Bullwinkle Show.