Minecraft Realms is being tested in certain Nordic countries at this time, and will be available worldwide later this year.
Minecraft Realms will be available for $13 per month. A Realms subscription allows you to invite other players onto your server, as long as they have a Minecraft account.
Minecraft Realms is not intended to replace large, public servers. The amount of players on the server will be limited, and a whitelist is in place so that players can only join by invitation.
As Minecraft Realms is currently in development, features are subject to change. More details are available on the Realms page at https://minecraft.net/realms
Minecraft Realms for Minecraft: Pocket Edition has been put on hold as of March 1st, 2014. We hope to have this service available later in the year. Full details can be found at https://mojang.com/2014/02/a-quick-update-from-the-pocket-edition-team/