There's a "setting" under options that says "Invited to Realms Alpha?". What is it? How can I tell if I was invited to it?
Minecraft Realms is a new paid service that allows you to quickly create worlds for you and your friends. Currently only available to anyone that attended MineCon and Swedish users.
Effectively they are dedicated servers, run by Mojang.
From the Realms FAQ:
Q: I can already see the Realms button on Minecraft: Pocket Edition. What’s up with that?
A: That’s there for selected testers. You’ll be able to host your own server soon!
The third way to get Minecraft Realms is to convince Mojang's servers that your computer is in Sweden. I did this using Tor.