Minecraft is a sandbox video game made by Mojang that's focus is around mining into the ground to find various metals, ores and materials, crafting and smelting them into different objects and building all sorts of fantastic buildings, structures and elaborate contraptions. Enemies, called mobs, come out at night and spawn in dark areas, so you'll need to keep yourself armed with bows, arrows, and swords, along with armor and you'll need to light dark areas as you mine down into the ground with torches. Markus Persson is the creator of Minecraft and goes by "Notch" on forums, in news and posts.
There are multiplayer Minecraft Servers where you can play with other friends and people so you have someone else to play with as well.
Another part of what makes Minecraft so popular is the great community surrounding the game and the Mods, Texture Packs and various other aspects of the game that let you customize the game and add a lot to how it's played. Overall, Minecraft is a great indie game that has limitless potential and loads of replay and fun.