If you're not too clued up on Minecraft, let's take this rather dry definition from the Minecraft Wiki:
Minecraft is a sandbox construction game... The game involves players creating and destroying various types of blocks in a three dimensional environment. The player takes an avatar that can destroy or create blocks, forming fantastic structures, creations and artwork across the various multiplayer servers in multiple game modes
The game has a huge following on PC, and is of course set to arrive on Xbox LIVE Arcade in the future (even speculative dates are not yet known). When the game releases it will have a 'beta' tag and will enjoy updates and expansion much in the same manner as it's PC brethren does.
Take a look at this trailer, though if you're familiar with the PC edition, there won't be much here that's new to you: