Sometimes I feel like something gets lost in translation when the English subtitles for Pan's Labyrinth refer to the fairy kingdom as the "underworld" (or the "Underground Realm," in the opening narration).
In one of the pages of Guillermo del Toro's notebooks featured in his book Cabinet of Curiosities, there's a note made by del Toro about beings called the "Mouros," said to live in underground cities. Del Toro goes on to note that in Galicia (where Pan's Labyrinth is meant to be set), it is believed that the mountains are hollow and contain underground realms and cities. So this is clearly what del Toro used as inspiration for the backstory involving the missing princess.
It's also interesting how the motion comics included in the DVD/Blu-Ray release of the film refer to the fairy kingdom as "Bethmoora," a place mentioned in Lord Dunsany's works (and, also, the name del Toro gave to the kingdom of the elves in Hellboy 2).
