This is a feature that was be added in the 0.9.0 update of MCPE. It enables you to explore your world without boundaries. Sadly, Apple products of the 4th generation and lower will not be able to experience this feature because 4g iPods and ect. have a single core processor, while 5g Apple products have double core processors, which can handle the infinite terrain. Note: 4g Apple devices can join any 5g devices in Multiplayer and experience the infinite worlds. It is also an option to expand your world without the infinite terrain. However single core processor doesn't just apply to Apple, any devices in general with single core processor won't have infinite worlds.
For Android, the infinite worlds are only available on Multi-core devices/tablets.
How to get it before 0.9.0
The server "infinity.lbsg.net" has infinite terrain without the 0.9.0 update. Click here to see the rest of the Liifeboat servers.
Note: These are the direct IPs, not the server names.
On twitter Tomasso says that infinite worlds can be created under "Experimental" in the app on single core processors.