I had literally no intuition for what the game wants you to do when I started. I wouldn't have figured anything out if I didn't look online because the game gives you no guidance beyond telling you to move with WASD and open your inventory with E. It's got two basic modes. Both of them will start with a random seed map that generates a unique world based on the seed number (you can input a seed number to get a specific map though). Survival starts you with nothing (although there is an option to start with a chest that has a few basic items) and you have to collect resources to build shelter and feed yourself before dark when mobs come out and will attack you. Early on the mobs are kind of frightening, but once you collect enough materials to craft armor they aren't nearly as dangerous. Beyond that it's completely sandbox. You just go around collecting the resources you need/want to build whatever elaborate infrastructure you want for shelter, farming, herding, enchanting, brewing, etc. There are some temples you can rob in the deserts, and I guess there are a few end bosses to fight as well, but that's about it. There is also a creative mode that allows you to fly and build with unlimited resources and mobs won't attack you either. All this can be single player or multiplayer, and multiplayer servers can do some futzing with the game structure to create new objects/abilities/commands if they want.
Honestly though, I don't know how people played the game when it first came out though. I'd hate to have to sit there and figure out recipes via trial and error. The first time I played I didn't want to look anything up and I died. A lot. I'd have gone nuts, especially if I had to figure out how red stone worked. The game allows you to create logic circuits by connecting red stone power sources to various things either directly or via red stone circuits, but I don't think I would have ever figured that out on my own (especially since my grasp on it is still very tenuous even after reading explanations...).
So yeah, you can build a world, but then it just sort of sits there feels special about itself, not like NWN where you could actually craft a story to play through. The soundtrack is surprisingly very nice and relaxing though. I think I expected 8 bit music or something with the art style...
edit:
This is probably one of the more interesting examples I've seen of a minecraft server altering the rules of play to create a minigame with it's own mechanics imo.