I'm wondering how to create a public server that anyone can join at any time. Is there a way to do this on an iOS device or do you need a separate application?
Using the iOS app alone (version 1.1.2), you can create a world on your device and play with other people who are on the same local wifi network. But the world is available only when the device that created it is running Minecraft, and it will be destroyed if you delete Minecraft from that device.
You can also pay to create a world that is hosted on an external service. This is called a Realm. You can create that world and subscribe to pay for it in the app. But to invite others to play in it, they will need to have Xbox gamertags, which I believe are always associated with Microsoft logins. Such a world is available to anyone you invite anywhere in the internet, and persists as long as you pay for it, even if you delete the app from your phone, I believe.