The Pokémon Center is a large red building on the West end of spawn primarily used for healing your Pokémon, but it also contains a lot of other useful elements.
As you enter the Pokémon Center you will be greeted by Nurse Joy alongside a Healer machine. Right clicking on her or the machine will fully heal the Pokémon in your party. You can also craft a healer using /recipebook healer.
To the right of Nurse Joy you will find a PC. Right click this to open up your Personal Computer where you can store your Pokémon in. You can also craft a PC using /recipebook pc.
To the left of Nurse Joy you will find the Trade Machines. Right click this to open up a menu to allow you to trade Pokémon with other users. You can also craft a Trade Machine using /recipebook machine.
The final section of the Pokémon Center is Dr. Book's EV/IV checker in the right corner. Right click Dr. Book holding a Pokémon of your choice to display its IVs and EVs in chat.