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.

One good way to get players thinking about their backstories is to pose each of them one question. For example, in my current campaign, all of my players had to tell me the answer to the question, "What one thing does your character wish for above all else?" Other good questions are, "What one thing does your character regret more than anything?", "Who would your character sacrifice his own life to save?", "How far would your character go to avoid death?", etc.

The thing all these questions have in common is that they make the character make a choice. Characters are defined by their choices more than any event or set of events in their backstories, so in order to encourage roleplaying, you need to force the characters to make difficult choices.

Note that the players don't necessarily have to tell each other these answers. In fact, you almost always see far more interesting RP when the players don't all know each others' stories already. Once the stories are out there, players often forget about them, stop playing to them, etc. They've been revealed; they're no longer interesting or relevant.

Instead, find ways to draw out characters' backgrounds and players' roleplaying bit by bit, over the course of multiple sessions. For example, instead of just dropping everyone's backstories into one session with a single trap or set of traps, you could have a door guardian who asks each character one of the choice-based questions above. The character then must decide how much to reveal - after all, if his answer to "how far would you go to avoid death?" is "become a lich if I have to", the character may not want to say that out loud in front of the party's paladin. He'll have to find a way to answer the question honestly enough for the guardian to allow him to pass, while still not giving away anything he doesn't want known - and I have years and years of experience that show that when characters know just a little information about a fellow party member, they will want more. And once that happens, you as DM can just sit back and watch the roleplay.