What special quality does a PC have that "normal people" don't have, and how could that be valuable to a big bad?

Everything in the character sheet is what they have special about them.

Think about it for a moment, a fighter is only able to swing his sword once every 6 seconds, one week of intensive level appropriate fights to take him to higher levels and suddenly he is able to use action surges with multiple attacks for a whopping 6 attacks in 6 seconds. These are not including movement and any other bonus actions or interactions that he does.

Same for a wizard. Today they are only able to cast a firebolt, tomorrow they suddenly get to stop time. Same for clerics, paladins, druids, rogues etc.. What do all of them have in common?

Experience.

That thing that piles up and then suddenly makes you hit harder, take more hits and do astonishing feats that any commoner would never dream of.

Everyone can pile up this "experience" which is a mix of both life force and magic that a creature has inside it. Defeating other creatures gives adventurers (unknowingly to them) part of their life and magic, thus making them stronger. A BBEG that would want to take something special away from them, would target just that... their experience which is what allows them to BE the heroes that they are. Take it away and they are no different than peasants.

I ran a game based on this once. Players were a bunch of nobodies in a world overflowing with heroes. They meet this strange critter along the way that is able to let them get more experience from villains and monsters. The catch is that there were more of these critters increasing the experience pool of all the adventures (thus the surplus), and when an adventurer who got their XP boosted turned evil, they would release massive energy to their god, making it stronger. Before the final fight, they had their experience drained and had to fight the final boss at level 1 until they found a way to get back their powers.

/r/DMAcademy Thread