The most important thing about Pern is not the dragons. The most important thing about Pern, the real gimmick of the world building, is Thread. There’s a whole lot of handwaving sciency stuff to explain it, but it’s not really necessary for the original trilogy. Basically, after a peaceful 200 year Interval (authorial capitalization) comes a fifty year long Pass during which this fungus falls from the sky in long Threads in approximately four hour storms. This fungus devours anything organic, including plastics. One strand can eat an entire cow. Or human. It destroys crops as well. And if it doesn’t devour, it injures, leaving long, thin scars.
Fortunately, their lifespan is very short – measured in hours – and life on the planet has evolved some defenses. This means that the planetary ecology has a chance to bounce back during the 200 year respite.
However, the need for shelter and defense has shaped the descendants of the human colonists of this world. It’s safest to be under stone, the more the better. Therefore, most people live in natural and man-made caverns in cliff-faces (Holds), in a feudal society.
The best defense against Thread is aerial assault with fire. Therefore, there is an air force composed of telepathically bound dragon/ride pairs. The dragons chew a stone that enables them to breathe fire and can transport almost instantaneously to any place they or their rider can visualize – or any time if it can be determined.
Because dragonriders spend their time fighting Thread and taking care of their highly intelligent partners in the volcano caldera they call “Weyrs”, they are dependent on support from the “Holds” and the “Halls” (where the various “crafts” – guilds – do their work.) This can and does cause conflict during the Intervals, especially since they also Search out potential dragon partners from these other groups. Obviously, it’s less of an issue during the Passes.
At the time of the first novel, there has been an unusually long Interval of 400 years, during which five of the six Weyrs disappeared, and many people doubt that Thread will even return so they don’t want to support the few dragonriders still around.
As noted above, dragons can travel between times, with suitable reference points. However, this can be very dangerous and it’s frowned upon unless deemed necessary. The turning point in the first novel and, really, the whole later series, was when the lead female character, and the ONLY female dragonrider at the time, went back the 400 years or Turns to fetch the other five Weyrs. This sets everything else in motion, including, eventually, the reason FOR the long Pass, but this only happens in books beyond the first trilogy.
The society is very hierarchical, with rank and Bloodline being very important. Major Holds are run by Lord Holders (almost invariably male, and while not quite primogeniture, usually a son or other male descendant or relative of the previous one), with smaller holds under their management in this very agrarian world. Crafthalls follow the apprentice/journeyman/master model, with each Craft run by a Mastercraftsman, equal in rank to a Lord Holder.
Weyrs have a much more complicated structure having to do with the color of one’s dragon, since color also determines the size and gender of the dragon. Basically, the rider of the large male (bronze) dragon who mates with the oldest female (gold or queen) dragon is the Weyrleader and is equal to a Lord Holder. Yes, the leadership is, by and large, male. (There are also, in size order, brown, blue and green dragons. Green dragons are infertile females. Only gold dragons Impressed (telepathically bind) female riders. I’ll get into this more when I talk about the sexual politics.