There are a lot of hidden similarities between what's happening in Ofelia's fantasy world and what we see going on in the human world: some big, some small, and some more apparent than others. (Sorry: there were no actual Fauns in the Spanish Civil War.)
But each serves to connect the human story of war to Ofelia's journey through the fantasy world.
So let's start with an easy one to spot: the walk through the woods. Ofelia's reading the Book of Crossroads and making her way to the giant fig tree. She is looking very pretty in her new silk dress and the lighting around her is warm with the sun and the music that plays is soft and gentle. She narrates from the book as she walks and there is a sense that she has, like Alice already entered into a wonderland.
Compare this to the soldiers, galloping on their warhorses through the undergrowth. Although they travel through the same forest as Ofelia, the scene is much more intense. We have the rapid, staccato beating of hooves and the music is much more violent.
This, combined with the horizontal wipes of the trees that transition seamlessly between these two woodland adventures, highlights the very different worlds in which the men and Ofelia live: a world of war vs. a world of innocence.
Locked Doors and Powerful Monsters
There are also some smaller parallels, like the importance of a key in each world. Pedro and Ofelia each receive a key that opens a locked door.
But in each case, that key betrays them. Ofelia's leads to the blade that the Faun will try and use against her brother, and the storeroom key will not only get many of the rebels killed but will also divulge Mercedes true allegiance.
Last—but certainly not least—there's a strong parallel between Vidal and the Pale Man. In the dinner scene, when Vidal invites all of his important guests over, he sits at the head of a sumptuously laid table. Vidal is obviously in control of the conversation. He shuts up Carmen when she reveals information he'd rather not be known and talks to the company about choice and the war.
When we first see the Pale Man, he's also seated at the head of a long table that displays a lavish feast. And just like Vidal, he is in control of his domain, not just visually, but in the manner of his actions upon waking. If Ofelia has created this fantasy world in her imagination, as some would argue, than perhaps her fear of Vidal has created this child-devouring monster.