I am about to show my age here, but what is minecraft? I see people on twitter talking about it a lot. I am guessing it is a game. That part I get, but I see "server" mentioned a lot. What server? for what?
Minecraft is an 8bit simulation game. You start as a person in a blank, randomly generated world. It is your job to create a habitat and survive against predators. It is quite addicting. There are also servers, like the ones that you are referring to. They make it possible for multiple people to play together at once.