In a nutshell, Microscope allows players to role play events in the history of the shared world, history that they are making up as they go along. Well, that might be a bit too simple of a description, so I'll try and see if I can do better.
Here's a bit from the book itself:
Microscope works differently than some other role-playing games you might have played, so let’s abandon some preconceptions:
You won’t have your own character.
You won’t play the game in chronological order. You may know all about the future, but be surprised by the past.
You’ll build the story from the outside in. You’ll decide the big picture, the grand scheme of history, and then burrow down and carve out the details.
It’s fractal gaming.
So think big: you have a massive chunk of history to play around in.
Well, that probably still doesn't explain it too well either, but it's closer.
Let's see, the is no GM. You need two to five players. You also need a hell of a lot of imagination.
After deciding on the beginning and an end, you start working on the middle - the history that takes you from start to finish. In a way, it really is that simple.
This is collaborative history building, with the twist that each player has a huge impact on the collaborative history that is defined throughout gameplay.
Heck, the overview of play takes up just a page. The concept is simple, but the result is a complex history that makes a world seem alive - or at least, one hopes you end with that result.
To paraphrase a fellow GM: "If during the world building, the players decide that The God King was slain with the Sword of the Sun and later, during the playing of the actual campaign set in the collaborative world players come across hints about the existence of the Sword of the Sun - they know it's history, they know the events surrounding it. It's a real piece of history".