Shadowrun is a game about being a criminal. Provided you are a criminal with an arsenal rivaling that of the government of a small militant nation. And believe me, you still don't have enough guns for what you're doing.
Basically, Shadowrun takes place in what is referred to as the Sixth World. It plays on the idea that the Mayans believed that every 5000 years or so, the old world would end and a new one would begin. The Fifth World, which we are living in now, ended somewhere between 2010 and 2012, depending on who you ask. The beginning of the Sixth world heralded the return of magic. And Dragons. And vampires. And just about everything you have ever had a nightmare/totally awesome dream about.
One of the major differences is the advent of "Metahumanity", which basically means we have a bunch of Dwarves, Elves, Orcs and Trolls running around.
On top of all that, something called the Matrix emerged.
No. Not that one!
The Matrix is basically a huge, complex, universal wireless network which everyone is constantly connected to all the time, 24/7/365. So yea, not much different than cracked.com (They're in your head!).
This all pretty much comes together to give you a fucked up place where it basically just comes down to who you want to be killed by: Nosferatu or Skynet?
The job of the players is go on what are called "Shadowruns", hence the game's name. A shadowrun is any kind of job done in the shadows. There will also be a lot of running. Usually away from the explosions. Usually.
Most of the time Shadowrunners will be hired by one company to fuck up another company. Perhaps Sony thinks Nintendo is doing too well this financial quarter. Enter the Shadowrunners who will, for a price, go and shoot, steal, kidnap or blow up anything of Nintendo's that you want them to.
Oh yeah. And if you fuck up on your mission?
Standard cop car is bigger than this, too. And usually has more missiles on it.
Shadowrun uses a Dice Pool system. This basically means that you roll a shit ton of dice.
Those dice right there? That's to see if you can find your pistol on the ground.
Essentially, you roll a lot of dice, count up the number of fives and sixes that appeared and if you have enough? Hooray! You're still alive!