It sounds like you're describing a bookmarklet which uses the Save Page Now feature of the Wayback Machine at https://archive.org/web/ .
Putting the following URL in a bookmark will make a bookmarlet which submits the current page to the Archive's crawler:
javascript:location.href='http://web.archive.org/save/'+location.href
When it's done, it will give you a URL to retrieve the page later, such as this one: