What does "[Country] out" mean in the context of a photo description?

Solution 1:

At a gross level, it means "not to be distributed in Japan"; that is, "Japan is out".

Background: the Associated Press is a news agency whose members and subscribers, themselves news organizations (newspapers, TV stations, radio, etc) both contribute news to and consume news from the AP; this aggregated feed of news is known as "the wire".

Generally speaking, paying members and subscribers of the AP are permitted to distribute news that comes across the wire to their local audience, unless otherwise specified. Here, "JAPAN OUT" is an example of "otherwise specified".

So an AP member or subscriber in Japan may not distribute that photo unless he calls his local AP office and negotiates a specific deal to do so, meaning he will have to pay an additional fee for the express permission to distribute the photo in question to his Japanese audience.

By the way, such strictures are not limited to the form "[COUNTRY] OUT"; you'll also see phrases like "TV OUT", "MAGS OUT", "NO INTERNET", "NO SALES", etc.

As for the reason, here's a brief explanation from a thread on a site dedicated to AP sports photographers:

Papers also tend to out competitors in their own distribution area so that an NY Times photo that moves on the AP wire will not show up on the front of the Daily News and compete on the newsstand for that point-of-purchase sale.

Note the use of out as a verb (meaning "exclude" or "kick out").