Blizzard is changing up the security on their authenticators a bit. This isn't a major change and shouldn't affect that many people. Starting now, if you happen to have multiple Battle.net accounts (not multiple WoW accounts under one Battle.net account), then each account must have its own authenticator. This means if you have separate Battle.net logins for email@example.com and firstname.lastname@example.org and you want to use an authenticator, you'll need to buy two. If you've just got email@example.com and all of your games are under that Battle.net login, then you're perfectly fine.
This is not retroactive. If you already have two accounts linked to a single authenticator, everything will still work as it does right now until you unlink that authenticator. The full blue post detailing the changes is behind the cut below.