Minecraft Realms is a paid multiplayer server hosting service, provided by Mojang, designed to be easily set up and used by up to ten players at a time.
Minecraft Realms website
Minecraft Realms frequently asked questions (FAQ)
Realms help resources
Minecraft Realms for Minecraft: Pocket Edition has been put on hold. We hope to have the service available later this year. Details about Pocket Realms can be found at https://mojang.com/2014/02/a-quick-update-from-the-pocket-edition-team
Having trouble with your Realms subscription? Contact customer support for assistance.