A protected world is a world that you can't mine or place things on unless the owner of the world has added you as a member. The vast majority of protected worlds are owned by individual players. You can tell which worlds are protected because in the world teleport panel they appear with a padlock icon on them.
All private worlds are protected by default. If you look through your owned worlds in the world teleport panel, they will only show with a padlock if you have made them public. It is possible to make a privately-owned world unprotected by using the /wprotected off command. This is an irreversible command, however, so be really sure you want to give up your world to the general public before you invoke the command.
Special Protected Worlds
There are also a number of premium worlds that are protected by the Developers. This means that only players who fulfill certain requirements set by the devs are allowed to build on that world. Such worlds include:
Still other developer-protected worlds are those that were created for a specific purpose:
Deepworld Auditorium Deepworld HQ Iron Arena Brass Arena HMS Challenger worlds