Why do these riding trousers flare out the way they do, and what is in them to create that shape?
I don’t think there’s anything in them to make them flare. I think it’s just the way they’re sewn. All the movies I’ve seen with men in jodphurs they seem rather deflated and not the way they’re drawn in cartoons.
Yeah, it’s just the way the fabric is cut. The bagginess is to give you extra room for your muscular horseback-riding thighs. When you get up in the saddle (English style), with your knees drawn up (as opposed to Western style, where your legs hang down more straight), it’s less binding if there’s extra fabric there, than if you were wearing regular-cut trousers.
Now, of course, they have stretch jersey riding pants. I know a number of women who wear jodhpurs simply because they’re slightly more flattering to those of us with “saddle bags” than stretch riding pants. 
As for the “why”:
Modern riding pants have a small percent of lycra to help with stretch/movement, instead of all that fabric. They are close fitting, like this:
http://www.statelinetack.com/images/product/in652978.jpg
And have a reinforcement patch at the inside of the knee. The most common materials for the patch are: a)the same fabric as the pants b)Clarino machine-washable suede c)Deerskin.
Also, in general they’re called Breeches (pronounced britches, as in, too big for your…). Nowadays, the term “Jodhpurs” is reserved for a certain type of riding pants only worn by children – they are designed to go with short boots, amazingly enough known as Jodhpur boots. The major difference between Breeches and Jods is that Jods have a finished cuff that goes over the top of the boot.
[Admiral Benson]
Ah… Many of you are wondering what’s wrong with my pants, well they started running short on materials right before they got to the knees so don’t give me any shit.
[/Admiral Benson]