Greyhawk is among the first fantasy settings published for Dungeons and Dragons. It wasn't the first, however. Empire of the Petal Throne, also known as Tekumel, was the first published campaign setting. Greyhawk was the first officially published setting (02/75) for Dungeons and Dragons. Finally, Blackmoor (published 09/75) was the first setting that Dungeons and Dragons was played in, but Blackmoor was the second official campaign setting book published for Dungeons and Dragons.
Greyhawk was Gary Gygax's campaign, which he co-DMd with Rob Kuntz. There were frequent cross-overs with Dave Arneson's Blackmoor campaign as well as Kuntz's Kalibruhn campaign, and many of the big characters in the games were actually player characters from one of his friends. Every once in a while, you can pick out something that you know could only make sense as part of a home campaign.
The World of Greyhawk is concerned with only the Eastern portion (The Flanaess) of the continent of Oerik of the planet Oerth. The Western portion of Oerth was never really well detailed. There was a map floating around of that area, with names very derivative of Earth names (Erypt, Ishtarland, The Celestial Imperium, The Nippon Dominion etc). This map was for Frank Mentzer's "Aquaria." The new D&D Chainmail rules are now set in that same area, but the world is completely different.
The opening of the Greyhawk Glossography (the boxed set which was later published for Greyhawk) begins by talking about trees. Strangely enough, that was what impressed me the most. The books look like they're part of a many book encyclopedia, written by Pluffet Smedger commissioned for the library of the Royal University of Rel Mord. It immediately convinces you that this is a living, breathing world. It details the seasons (which have their own names, depending on which group is talking about them), the cycles of the moons (Greyhawk has two: Luna and "her handmaiden" Celene), and the nations and heritages of its people.
Greyhawk is also the name of the largest city on the continent, which I will detail better under Free City of Greyhawk (unless someone beats me to it). Surrounding this city are many different nations, all with their own history and backgrounds. Since the first publication of this world, the demon God Iuz destroyed most of the nations, he was beaten back during The Greyhawk Wars, and then new nations rose from that carnage of the wars (From the Ashes).
A lot of the conflict in Greyhawk isn't about Good versus Evil, but Law versus Chaos, or Nation against Nation, or even ethnicity versus ethnicity. Keep in mind, there still is plenty of Good versus Evil going on here, it's just that you're not positive that Good is going to overcome, because they can't always work well together. (The same can be said for the Evil, luckily.)
Speaking of ethnicity, the natives of Greyhawk are descended from different backgrounds: Olman, Flan, Oeridian, Sueloise, Baklunish, and Rhenee. The Flaeness was originally populated by the Flan. When the Oeridians started to migrate eastward, they displaced the Flan tribes to a degree. Later, the Suel and the Baklunish empires managed to destroy each other in the "Invoked Devastation" and the "Rain of Colorless Fires", and so they moved out of their now uninhabitable homelands further east, displacing both the Oeridians as well as the Flan. The Rhenee wander through these societies, a gypsy-like people from somewhere unknown, but not of Oerth. Finally, the Olman are from a nation much further to the south. There are other peoples, including the Ur-Flan, but I have much less information about them.
Greyhawk is also known for its celebrities. Most gamers have heard of Vecna. In addition, they probably know about Lolth (though, they may spell her name Lloth as per the Forgotten Realms.) There are also spells, monsters, and artifacts named after famous Greyhawk personalities: Mordenkainen, Bigby, Otto, Tenser, Rary, Quaal, Kyuss, Keoghtom, and Melf. Greyhawk also is best known for its gods, of which the list in the Third Edition Players Handbook is only a subset (Greyhawk has MANY gods, including "Hero-Deities" which are people about a half-step shy of true godhood).
With Third Edition, Greyhawk again becomes the "default setting" of Dungeons and Dragons. This basically means that the gods from Greyhawk are the default ones used. Honestly, not much else is actually affected by this fact. The history of Greyhawk is now the responsibility of the RPGA and the Living Greyhawk campaign. Each area corresponds to one of the countries. I live in Michigan, so my corresponding location is Furyondy.
I am going to list a few of the nations of Greyhawk. This is by no means an exhaustive list, and I'll try to add new nations as writeups get linked here. If you want to detail one of the nations, please /msg me and I will add your writeup to the list below. (Also /msg me if there's something else I should add here. I could write much more, but I would recommend picking up the Living Greyhawk Gazeteer for more information. Or buy a few of the ESD available from Wizards of the Coast. Or read the Gord the Rogue novels by Gary Gygax, and skip the Rose Estes novels. There's a lot out there.)