What makes the game Minecraft so famous?

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Its a game about surviving by crafting items using blocks. The world is a bunch of blocks. U punch the tree to get the wood you get the wood to make da cabin. Its famous i guess because it's fun to build stuff and fight stuff and survive with your friends.

Create a large scale world out of pixelish blocks and have it work.
plus the ability to build ANYTHING out of said blocks.

the Normal Game (non-story) has two basic modes
1. Survival. Which is what it sounds like. Your dropped into a random spot on a random map with nothing and have to survive the swarms of monsters that come out at night

2. Free Build Mode.
Random map, customized map or just a blank space. Open access to any and all mats items and everything else.
Complete freedom to build ANYTHING. Monsters do appear but arnt hostile.

When I say you can build anything I mean anything. Check some of the lists/vids on youtube.

Minecraft is so popular because of the creative freedom it allows you. There are two main modes, survival and creative.
survival drops you off in a massive world and you are left to your own devices from then on. Most players will start to make a small base, make basic tools and items like a bed and chests for storage, and start exploring. But if you wanted to, you could be nomadic and just explore. There are enemies to fight too, but it's worth it because many enemies will drop items that help you to make useful items. It can be really satisfying to plan and work towards creating a large project when you need to find, farm, or otherwise create it all from scratch
the other mode is creative. Creative mode gives you access to all the items and blocks in the game with no limit so you can just focus on building something cool. You don't need to worry about how you get all the items or worry about getting killed by an enemy and dropping whatever you're holding in your inventory (although you can change the setting in survival mode so you won't drop stuff when you die)
people also create lots of different challenge maps for other people to play. These can be things like solving puzzles to open up doors to new rooms (i used to watch a lot of yogscast videos where they played a lot of these), falling from a long drop into a small bit of water, even full stories told through signs
minecraft is popular for similar reasons that animal crossing is popular, freedom. There's no strict story, no strict goals, and no real end to either game. Both games are what you make of them