Minecraft is a game written in Java created by Mojang AB in 2009. Minecraft has two current variants - Classic (which is free) and Beta (which you have to pay for).
In Beta, the main goal is to survive. At night, monsters spawn (but not in Peaceful mode) and attack you so you need to craft items and tools to help you survive. You also need to eat regularly.
Minecraft has gone through many development stages:
Classic - the oldest version. It is still playable and has multiplayer. In Classic, you have an infinite amount of blocks, no health, and no mobs.
Survival Test - Part of Classic, very basic compared to the Survival we play and know today.
Indev - Added a number of new features, including crafting, torches, and tools.
Infdev - Added the ability to have an infinite playing surface.
Alpha - Added biomes, nether, sneaking, and much more.
Beta - The current version of Minecraft. Added beds (which can skip the night), more mobs such as endermen and wolves (which can be tamed with bones and attack monsters), and many more.
Multiplayer is in both Classic and Beta, which allows, well, multiplayer, duhhhh
Girlfriend: Why aren't you spending much time with me, Greg?
Greg: SHUT UP AND GO AWAY, I'M PLAYING MINECRAFT