Minecraft PE Servers

General information
Just like Minecraft's desktop edition, Minecraft: Pocket Edition also has support for external servers.

Making Minecraft pe servers
Mojang offers the Realms platform which allows users to to easily host their own MCPE server, this approach is the easiest but it has the limitation that it's whitelist only and that it has few features for customizability.

You can download PocketMine from https://pocketmine.net to host your own Minecraft PE Server, this will require you to rent a VPS or dedicated server from elsewhere to run the server on, which may add significant complexity.

Alternatively you can use on the instant hosting solutions like https://www.mcpeservermaker.com

which has apps that allow you to start your own MCPE server in just one click.

Finding Minecraft PE Servers
If you are merely looking for MCPE Servers to play on, check out a server list like Minecraft PE Servers