1. The WABAC (pronounced "wayback") machine (pictured above) was from the Peabody's Improbable History segment of the early 1960s cartoon series The Rocky and Bullwinkle Show. The machine was constructed by Mr. Peabody, a professorial, bow tie-wearing dog, to be able to visit famous historical events. At the request of Mr. Peabody, Sherman, Peabody's "pet boy" assistant, would set the WABAC machine to a time and place of historical importance, and the two would be instantly transported there. The machine apparently later returned Mr. Peabody and Sherman to the present, although the return trip was never shown in the cartoon segment. The machine was little more than a plot device to allow the characters to visit the past.
The name WABAC is a play on computer names such as UNIVAC and ENIAC that were contemporary to the Rocky and Bullwinkle Show, and the WABAC machine was similar in size to those early computers.
2. The Internet Archive uses the term "Wayback Machine" as the name for its service that makes archives of the World Wide Web. This service allows users to see archived versions of web pages of the past. The use of the term "Wayback Machine" in the context of the Internet Archive has become so common that "Wayback Machine" and "Internet Archive" are almost synonymous.
The Internet Archive has millions of website source code saved in a gigantic database. You can use the service to see what your favorite sites used to look like, grab source code from sites that you changed the code for and want to get back a cached version, or visit sites from the past that are no longer around today.
For example, here's the first archived homepage of the NY Times, from December 30, 1996:
Here's Yahoo's first homepage in 1996:
And Google's first archived homepage in 1998: