A coherent and richly detailed world where much of the back history can be learned in dialogue, gleaned from mission objectives and locations, or through voluntarily read documents. A lot of Game Masters either fall so in love with their history and write up so much of it that they require the players to learn all of it or neglect it entirely. While there's nothing wrong with coming up with a 75 page setting document, you have to come to terms with exactly what writers and game designers have been learning for years. The audience, or players, will only see about 5% of the effort you've put into the game and that's okay.
So what to do with it if you've got it? Weave it into the setting, the NPC personalities and behaviours, the missions and the environments, the monsters and the artefacts left behind in the dungeons, and perhaps create a few brief props here or there or allow appropriate Knowledge checks that reveal the juiciest tidbits when they arrive at a new location. If you have more information than those tidbits, feel free to offer the players more information.
"Okay, so you rolled 25 on Knowledge Local about this town. You've heard that the two honey mead companies are staunch rivals and that the windmill was recently built by some grateful wanderers who were given refuge here for a month during a terrible snow storm. The farmers are pretty protective over their chickens as they believe that the egg is sacred to their Gods. Would you like to know more?"
If they want to know more about the honey mead, then give them a one minute spiel on it (if you have a full minute of it). Or if they want a brief expansion on all those other three then you can do the same there. Don't deny the players the chance to learn more as they might be quite keen on it but also don't assume that they want to sit there and listen to five minute speeches. Odds are they won't be able to remember that much anyway so if you have something that really deserves five minutes - i.e. a religious festival - than work it into the storyline. Have them arrive during it. Or have them try to stop it.
What if you don't have much setting to play with and don't want to put in the hours to create some? Pick up someone else's rich world setting and read up on it. Pathfinder has a very rich and interesting world in Golarion - though some of the countries still have few details released. Skyrim itself is a possible game world you could run. Then there's the numerous fantasy series that you may have read or watched that you could co-opt.
If you want to create your own setting but don't know how then go to the various fantasy writer resources online about creating your own game world. Heck, just google 'fantasy world creation guide' and you'll get several options.
Skyrim is also a very beautiful and very expansive world so brush up on your descriptors. If you're not so good at improvising it alongside everything else, then jot down your location descriptions on small pieces of card so you can easily flick between them. It also looks less messy than having a whole page in front of you and it can be easier to arrange them. Especially if you number them and then tie those numbers to an overall map of the location that you place in front of you.
Remember to make such descriptions evocative and focus on the telling details that can suggest many other details rather than simply going through a shopping list of what, precisely, is there. Again, how-to-write advice covers this better than I can (as they have whole articles and chapters devoted to it) but here's an example:
"The windmill stands twenty feet from the two Honey Mead places that are on either side of it. The cobblestone road is five feet wide and there are five chicken farms on one side of it and the Honey Mead places and the windmill on the other side. There's a town sign that stands beside an old cart filled with barrels."
To make it evocative of a safe place you might have:
"A rustic sign hangs over an old barrel-filled cart as you come in along the cobblestone street. Chickens cluck quietly as they scamper across the farm yards to the left of you, digging amongst the grasses. One has even gotten into the fenced off kitchen gardens and is quickly digging up the carrots to get at the bugs. On the other side stand two almost identical Honey Mead businesses, Bees 'R Us and Sweet Brew, which flank a windmill that creaks in the warm spring breeze."
On the other hand, you could make it seem dangerous by writing:
"A weathered sign hangs crookedly over an old barrel-filled cart whose wheel has rotted and burst out from under it. Chickens dart across the cobblestone street, making their way loose from the broken down fences. The windmill creaks in the icy breeze but the fans are too shredded to catch enough wind to turn. Honey Mead businesses flank the windmill, mostly hidden behind a high stone wall topped with outward facing spikes."
All of these descriptions give the same locations, objects, and visible animals but each one imparts something different. The first is pretty ordinary and doesn't give much away. It has no emotional depth. The second one raises a number of assumptions of quaint cottages and friendly rivalries. The third one suggests a poverty stricken town that may well be under siege from something. Perhaps the rivalry is a little more intense?
If a regular picture is worth a 1000 words, this one is worth a million.
The other trick of Skyrim is that you can do very ordinary work if you would like. Why not try your hand at being a lumberjack? In a roleplaying game, you could always pass a couple weeks with a few rolls and some relevant 'this happens' comments from the Game Master.
You can also overhear comments from the local townspeople and see them go about their business. A little trickier to do as it tends to draw the players' attention and lead to assumptions that it's important, if you focus on the dialogue rather than character descriptions than there more likely to pay attention to what is said rather than to who is saying it. Just describe that 'two merchants stand by their stalls talking about how the recent frosts have damaged their crops' or if you want to draw all the more interest to it than actually act out the dialogue (perhaps with your left hand up when you're one person and your right hand up when you're the other). Yes, the characters might go and talk to them but that just adds to the immersive experience.
Now of course the game is a sandbox one so having multiple adventure hooks (ideally getting the players to list them so they don't forget) and multiple adventures at hand (or an ability to improvise) is really important. Improvisation is probably your best bet as it means you can just slowly draw out the map as they explore it. Bestiaries (or Monster Manuals) and sets of NPCs at different levels will all be very useful to this. I talk more about sandbox games and techniques in the Fallout 3 article I've done earlier.
A campaign based around Skyrim, or including elements of it, should appeal to Explorers who will adore roaming around an entire country and discovering all of the interesting bits and pieces hidden within a richly drawn world. Their main drive is to have a new experience after all and they'll be happy to meander around and take the plots as they come, choosing whichever one seems to offer the most unique experience. Action Heroes will adore the sword and sorcery angle and will be quite happy to explore dungeons, kill beasties, and engage with whatever social conflicts or wars are going on. They'll certainly approve of any interesting approaches or settings you throw them into as they do enjoy themselves a setpiece battle more than most.
Communicators would love it, too, but will likely want to enjoy some Day In The Life style plots where they can simply indulge their senses and see what it might be like to actually live in that world. Expect a lot of conversations and some attention on the more mundane aspects. These guys could well enjoy just being a lumberjack for awhile and actually roleplaying it. Tacticians will want a bit more flexibility to pick out the most efficient and effective way for dealing with threats so try to bear that in mind when you design dungeons by including possible stealth passages, hidey holes, and methods of poisoning or otherwise taking out some of the enemies with minimal risk.
Investigators will have the least to gain from a Skyrim game per se but could still get a lot of enjoyment in a fantasy world like Skyrim. You'd just need to include more mysteries that require solving and more clues that there's something bigger going on - such as conspiracies, assassinations, and other such details.
You can find the trailer for the game over here. If you'd like to read the sort of tropes that Skyrim used, you can find them here.
For the next Game Translation, you have a choice of these: Left for Dead, Half Life 2, Silent Hill, Project Zero, The Suffering, Gears of War, Mass Effect, Dracula: Origins, Realms of the Haunting, Dragon Age 2, and pretty much any survival horror or horror game. If no one picks anything by next week, it'll be The Suffering.
If you want to see the list of games I've done thus far, you can find the Game Translation series starter over here.