We want to make it so you can't just take things off the net and put them down the memory hole
—Internet Archive founder Brewster Kahle, presentation at Dodging the Memory Hole 2017
The Wayback Machine is a section of the Internet Archive. What makes this website so notable is that, while the Internet Archive is, well, an archive of the Internet, the Wayback Machine allows people to actually access past versions of web pages.
In other words, it's the browser version of a time machine.
Here's how it works: after accessing the WM website through the link at the top of this page, users can paste a URL address on the input-box next to the "Take Me Back" button, and then, after clicking said button, the user is shown a calendar-like list of archived pages (provided there are any). Dates written on blue dots are links to versions of that particular page archived on that particular date.
The site proved to be a boon in (re)constructing the All The Tropes wiki, as TV Tropes had developed a nasty habit of deleting either examples or entire articles themselves, without even having the common courtesy to keep a page history around for reference. (Even legitimate tropes have gotten the axe, just because they couldn't stop people from potholing to them.)
This link leads to the results for the TV Tropes Main Page in the Wayback Machine; changing the URL posted to that of either existing articles or Permanent Red Link Club members, you can access the site and reminisce about how it used to be, before it fell from grace. Or rescue material that has yet to be restored here.
- Or who needs to download something from a site that's gone away.