Minecraft is a sandbox of sorts where your only goal is to survive. You start with nothing then chop trees make tools and with them mine more materials. Those materials can be smelted into ores to make better tools, and more useful items. Eventually, you get to the point where you've built railroads, houses, farms and other interesting stuff.
The only problem is that at night, you die.
There are creatures which inhabit the night in Minecraft. Evil creatures. Dangerous creatures. Creatures that go "boom". And you realize quickly that survival isn't as easy as it seems.
It's actually a really great game that my daughter is much better at than me. We've wasted dozens of hours dedicated to constructing this or that.
She has also discovered a special version of the game called "Tekkit" which allows you to bring the Minecraft world up into the computer age. I'll be honest, it can be a little glitchy, and you need to know a little about programming to make it run completely smoothly. But the two most recent items she and I built were two "mining lasers" (handy for zapping the occasional creature) and jetpacks. Our base there is surrounded by a force field, and connected to the neighboring village by a high speed rail. We have also hollowed out a nearby volcano to serve as our lair, and we have built 'teleporters' to zap us back and forth to it.
We're still working on the sharks with freakin laser beams.
There are online servers, but my daughter and I usually stick to a server I set up for her and her friends. Here's a little look into what the original world of Minecraft looks like.