Even though you said you figured it out, for the benefit of those unsure it means that character is in an instance or dungeon, usually through the Duty Finder, which indeed switches your character onto a specific Duty Finder server (hence the term 'Another World', as servers are called 'Worlds' in FFXIV). Once the instance or dungeon is over, that character is returned to their home server. Hopefully this isn't too confusing.