Taken from Minecraft.net:

Minecraft is a game about breaking and placing blocks. At first, people built structures to protect against nocturnal monsters, but as the game grew players worked together to create wonderful, imaginative things. It can also be about adventuring with friends or watching the sun rise over a blocky ocean. It’s pretty. Brave players battle terrible things in The Nether, which is more scary than pretty. You can also visit a land of mushrooms if it sounds more like your cup of tea.

Best way to learn Minecraft is to watch others play it!

What is Minecraft?

Minecraft can seem really daunting at first. It's a sandbox game, which means it doesn't have a set mission or objective. It allows a player to freely roam the virtual world, doing as he/she pleases. This appeals to lots of people because it allows for endless creativity. Just search Google for Minecraft builds, and you'll see many different creations, from recreating known universes (such as recreating kingdoms from Lord of the Rings) block by block or by detailing a block house with Minecraft items.

What can be done in Minecraft?

More than you'd think can be accomplished in Minecraft! Here's a SMALL list: