Minecraft is a first-person fighter/sandbox construction game created by Mojang AB.
Not a bad game. The dev of it though seems to think it's almost finished.. IMO, it's far from it.
Minecraft (Single Player) as is, is pretty much:
1) Gather resources.
2) Build / Craft with those resources.
3) Go to 1.
Why can't there be some seed generated towns, npc's, dungeons and quests too?
The game really isn't optimized well either. You'll probably have better luck running Crysis than Minecraft.