Factorio is a crafting game centered on automated production. You create factories which turn raw resources (ore, coal) into bigger and greater products (electronics, weapons, more factories). So you'll do something like set up a mine which transfers ore to a furnace area, which smelts it into bars, which then are turned into useful products. Sounds like usual, except in Factorio the number of resources (iron, copper, etc) you'll use in a game is on the order of 100,000. A TON of product, made easy since it's all automated. The magic of Factorio is that all of this factorymaking is very simple. There are only a few tools, but as the game progresses you will organically learn more efficient ways to use them. You will adopt a style for your factories, which will be different than the next person's. Comparing and sharing factory designs is a really neat part of the game, which you can experience in the multiplayer.
Of course, there are enemies that will try to impede your progress, the neat thing in Factorio is that their aggression is based on the amount of pollution you make in your factories.
The game is still in development, this review is based on the v0.14 experimental release. A free demo is available if you're interested.
As a sandbox game, you can't really "beat" Factorio, but there is a win condition, which you'll reach after 15-25 hours (The range depends on how experienced you are, if you have friends helping you, etc.)
Update: Factorio v 0.15 was released.
I neglected to mention the progression system in Factorio because I didn't deem it necessary at the time, but now it is relevant when talking about 0.14 > 0.15 changes. In Factorio, you progress the game through research, which unlocks recipes for more objects such as better guns or unlocks the utilization of a new resource. Science is done by building science "packs" and processing them in a lab. Eventually you research how to build a rocket and launch a satellite into space, which is the win condition. 0.15 changes dramatically the recipes (and complexity of said recipes) for science, which means you'll need to build more complex factories to output these more complex science packs, which is a good change overall, and made the game fresh again for me when I played it.
0.15 also introduced nuclear power, which isn't really necessary - you can get through the game without it, but adds another thing you can do (the setup is fairly complicated and unique) and gives the devs an option to add some extremely power-intensive options for additional lategame content.