So, what is Minecraft?

Minecraft is an independently developed video game created by Markus "Notch" Persson.  Based on the Java programming language, the game is considered a "sandbox" game. It provides players with a large virtual world consisting of blocks of various materials (dirt, stone, iron, wood, etc.) that can be broken down and crafted into a variety of tools and structures.  

Currently, the game offers two basic modes of play:

Classic - the simplest game mechanics are used.  Players have an unlimited number of blocks with which to build.

Beta - adds a great deal of complexity to the basic mechanics of Classic mode.  Here, players collect resources and develop new items through a variety of recipes.  This mode also allows for "monsters" to be added to the game world.

To learn more, read the Wikipedia article on the game and its history.

Here's a fan-made trailer for the game: