What does 'white-listed' mean when I can't connect to a minecraft PE server?

White-listed means that the server is only accessible to people the server owner has specifically allowed in. The only way to join is to contact the server owner and ask - they may or may not let you join.

A Whitelist is the opposite of a Blacklist. A server with a whitelist only allows people on the whitelist to link to it, everyone else is refused. You will have to get in touch with one of the server's admins to get your name added to the acceptable list.

The whitelist is a list of players which are allowed to be on that server. It means that you aren't on that whitelist. So you can't join. You have to ask the owner