It’s a sandbox game. You basically use the environment to build things. There used to be several versions of the game, classic/survival, indev, infdev, and now Alpha. Alpha is what is being maintained, and it pretty much has all the other things the previous games had.

Basic gist is, if you don’t change the difficulty setting to “Peaceful”, then you have to build a home/fortress/base during the day to hide from the monsters that come out at night (which include arrow-shooting skeletons, spiders, zombies, and the above creeper). Creepers don’t make any noise when they are near you (unlike the other enemies in the game). So in the above youtube link, the creeper just walked right up to the player and before he could react, self-detonated.

If you play the game in Peaceful mode, you basically just explore/mine/build stuff. You might run into a slime at random, due to a de-spwaning bug, but that mode mimics the old Creative mode.

The whole point? Use your imagination. Each generated world is yours to do whatever you want with (in single player). In multiplayer, same thing, just with friends. Although griefers can come and spoil your fun if you don’t watch the server.