BackupURL creates, archives web snapshots
Just copy and paste a URL and press the backup button, and a truncated link is created for you. For example, the TSN page above - its content has likely changed if you visit the original link, but the BackupURL snapshot is perfectly preserved.
There are some limitation. It shouldn't come as a suprise that some Flash elements and embedded videos won't be captured. Still, BackupURL is a handy way to capture pages where content changes frequently.
There isn't much information on the site just yet, so I wouldn't recommend using BackupURL for archiving anything of critical importance. At least not until they provide some important details like how long your snapshots will be saved.