It is a badass game.
Basically each hex is a resource. You put two settlements in between the hexes. Each hex has a number - 2 through 12, assigned randomly. There are forests (wood), mountains (rock), meadow (sheep), clay (brick), and field (sheep). There is also a desert that produces nothing where the bandit lives (more on that later).
On a player's turn, you roll two di. Their total determines which hexes yield a resource on that turn. So if you rolled a 3 and a 3, you get a 6. Any hex labeled with 6 produces. If your settlement is near it, you get a resource. Generally, anything with a 6 or 8 will produce the most, since those are statistically the greatest to be rolled.
You then use these to build things, such as roads or cities (an upgraded settlement). You can also use them to buy development cards, which can give you special outcomes. One might let you build two pieces of road instantly. Another might give you a soldier for your army. Another might give you a victory point.
The goal of the game is to get 10 victory points. For each settlement, you get a point. If you have the longest single road (of at least 5 segments), you get two points (this can be lost to other players if they build a longer road). If you upgrade your settlement to a city, you get 2 points and that city gets double resources. If you have the biggest army (of at least three soldiers) you get two points.
So having two settlements, a city, and the longest road would be 1 + 1 + 2 + 2 = 6.
If you get a development card and it's a soldier, you get to move the bandit to any hex you want. While he's there, resources stop being produced. This is a good way to cripple your opponents. Also, when you move him, you get to take a resource card randomly from that opponent.
That's really all there is to it.
Why is it so awesome? Because it's random. The locations are randomly placed, as well as the hex numbers. A typical game might take 45 minutes to an hour or so depending on what happens.
There's more to the game than that, but this is a quick crash course. I only just discovered it last Christmas and it is VERY fun. I am trying to get a copy myself so I can teach my friends and play it. I might even do the online version through MS Zone.
Needless to say, it is an incredibly addictive game. Simple, but can get very engaging.
Edit: In that screenshot, I'd wager blue stands the greatest chance to win. He has the potential to build a massive road, and his settlements give him access to all 5 resources. Red and Grey both lack one of the resources. Orange just has crappy positions, except he is rolling on two bricks, which can be very handy down the line when you want to start trading with others.
