Saffron is the dried stigma of Crocus sativus, and its price is a matter of arithmetic rather than mystique.
Each flower produces exactly three stigmas. They must be picked by hand, from flowers that open in a short autumn window and are gathered at dawn before the sun degrades them, and then dried. Something in the region of 150,000 to 200,000 flowers, and correspondingly a very large amount of skilled hand labour, yields one kilogram of dried saffron. There is no mechanised alternative, and there has never been one. That is the entire explanation of the cost.
Crocus sativus is a sterile triploid. It does not set seed and cannot reproduce sexually; every plant is propagated by dividing corms, and the entire world crop is effectively a clone descended from an ancient selection. Its wild ancestor is generally taken to be Crocus cartwrightianus of the Aegean. This means saffron is a human artefact in a strong sense: it exists only because people keep dividing it, and it would vanish without cultivation.
The colour is crocin, a carotenoid of unusual water solubility, which is why saffron dyes an aqueous dish and most carotenoids do not. The bitterness is picrocrocin and the aroma safranal, formed from it during drying.
Because it is expensive, saffron is the most adulterated spice in commerce, historically and now: safflower, turmeric, marigold petals, dyed fibres and coloured threads have all been passed off as it. Medieval Nuremberg operated the Safranschou, a formal inspection code with severe penalties, including burning, for adulterators.