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 discussions on the Minecraft Forums
Minecraft Realms for Minecraft: Pocket Edition has been put on hold as of March 1st, 2014. 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.