Minecraft is a sandbox game which allows players to build constructions out of textured cubes in a 3D world. It is currently in development by Markus Persson, aka "Notch". The gameplay is inspired by Slaves to Armok: God of Blood Chapter II – Dwarf Fortress, RollerCoaster Tycoon, Dungeon Keeper, and especially Infiniminer. The game is split into two variants, Alpha and Classic; Classic is both single- and multiplayer and includes only the building aspects of the game with unlimited blocks, and Alpha also has a single- and multiplayer mode and includes monsters and a much greater variety of crafting available, as well as requiring players to mine their own blocks.
Minecraft features two separate game modes, each focusing on the core mechanic in a different way: Survival mode and Creative mode. Creative mode is solely a building simulator, playable in single or multiplayer mode. Survival mode adds monsters as well as many other features.
Source: Wikipedia, "Minecraft", available under the CC-BY-SA License.