The answers are mostly in the screen that the Realms button shows you (emphasis mine):
Welcome to Minecraft Realms Beta!
We're still testing out features, but
eventually Realms will let up to 10 Pocket
Edition users play together online. It's
currently free, and limited to a set
amount of servers.
So Realms is a way of playing multiplayer with other players over the Internet – using a Realms server, you don't need to be on the same wifi network. To make that work, Mojang has to run servers, but since this is in beta now, there are a limited number of servers. When it says "No available servers", that's PE telling you that all of the Realms Beta servers are already being used by other PE players.
The way you join a local multiplayer world has changed, but you can still play multiplayer on local wifi. That's good, because Realms will be for-pay once it's out of beta.