The Known World in question is the default setting of all the modules TSR released for the Basic D&D games of the 1980s. I was never a devotee of that setting, as some people became, but I remember it for its role in the beginning modules from the Basic and Expert sets, and from a 2e AD&D campaign set in Mystara, as the setting became known after it was converted to that game.
Laurence Schick, the co-creator of the Known World with Tom Moldvay, has an article about the development of the setting at The Black Gate. The most interesting insight to me was the fact that they began developing the Known World shortly after Moldvay acquired a White Box set of OD&D. This may make it the first fantasy world consciously created for Dungeons & Dragons. The World of Greyhawk, under the name The Great Kingdom, existed pre-D&D as a setting for wargames. The Forgotten Realms existed for years before 1973 as a setting for Ed Greenwood's unpublished fantasy fiction. But the Known World was created after exposure to D&D, specifically to serve as a setting for D&D adventures.
The article is also notable for demonstrating the design of a world for specific objectives. Schick and Moldvay originally designed the Known World to be a shared world for multiple DMs in northeastern Ohio. Thus, it includes a great many cultures, all of which are extensively detailed. Though this expansiveness and level of detail dovetails with the demands of a commercial game setting, it looks like TSR actually shrank the Known World for their official version. Unfortunately, the article doesn't mention why that decision was made or which countries were lost in the transition.
You can read the article here: http://www.blackgate.com/2015/02/07/the-known-world-dd-setting-a-secret-history