From my own experiences, I would suggest three primary guidelines to follow:
1. Focus on the major concepts
When describing your world, focus on the major concepts and avoid dwelling on details. Details can and should become important during the game itself, but when the players are learning about a brand-new setting, they need to see the big picture first in order to make sense of it.
Players are usually good at filling in the blanks by themselves. For example, if there's a bitter feud between two criminal organizations in Capital City, it's often enough to devote just a sentence or two to this fact. The players will understand the implications of a large gang war without being told about specific battles fought and certain tactics used.
2. Emphasize the differences
When focusing on the major concepts, particularly emphasize those that make your setting different from similar settings. If a major concept of your D&D campaign is that there are many dungeons and dragons, you probably don't have to explain this in much detail (or at all), because it's not very different from other fantasy settings.
At times, this may in fact conflict with your idea of an in-world character giving the description: If the entire world is always covered in snow, the world's inhabitants won't find it strange but your players surely will. To avoid this, you could have an outsider of some sort give the description. In this way, the most striking differences are plainly spelled out for your players, who have no previous experience with the setting. Some type of "letter home" is a recognizable and effective way to accomplish this.
3. Keep it brief
Above all else, keep your written description brief or most players will have a difficult time following it. This is not because they are lazy or stupid; taking in several pages' worth of completely new information is difficult for anyone, especially when it's a hobby and not homework. Devoting a page or less to the description is usually enough to get your point across without giving the players too much to read.
There is an exception to this: If you know that all of your players do enjoy long written descriptions, you can ignore this guideline. However, if even a single player finds them tedious, you should keep it brief and feed the players more detail later on.
Bonus guideline: Use humor
This is not essential for writing a good description, but it can make things more fun for the players: Try to use some humor in your description. It doesn't have to be elaborate or even very funny to be worthwhile—anything that encourages a smile is usually enough. For example, in the e-mail briefings for my recent Star Wars campaign, I included short in-universe advertisements to add just a little dose of humor before every mission.
Bonus guideline: Use regional slang
If your world contains slang expressions that you intend to use in-game, a written description is a great place to introduce them. By having your narrator toss in a slang expression and explain it briefly, you're not only establishing a particular word but also the fact that you intend to use slang in your campaign.