The pvp world is a separate world that you can teleport to. It is accessed using the /world command. When used in the overworld, /world will teleport you a random location in the pvp world, and when you use it in the pvp world it'll teleport you back to where you were in the overworld.
It is only possible to use /world when no player is within 50 blocks of you. It is not possible to set beds in the pvp world.
To get a list of people currently in the pvp world, type /pvplist.
The pvp world has always had a border, which has varied from 1k to 150 blocks, and is currently 250 blocks (making the world 500x500.)
The pvp world is reset on the first day of all even months. So December 1st, February 1st, etc.
Some old copies of the pvp world can be downloaded.
The source code for the plugin providing the /world command is available on github.
Read Custom PvP worlds for info on what is needed to create custom pvp worlds.