If you pull out the "padded" piece inside of a shoe or ski boot, that thin pad is the footbed. If you put it on the floor and step on it, you'll see exactly how much support it gives your foot (none!). The boot board (the piece of plastic inside the boot that the footbed sits on) is a hard, flat piece of plastic. The footbed provided with the boots is almost always a complete joke. Usually about 1/8" of flat padding. The boots I got last year (Lange 130s) did have a more substantial footbed, but still not to the level of a custom footbed. With the stock footbed, you are standing on a flat piece of plastic (with some padding) and trying to manipulate a 5+ foot long ski that is sliding across on in the snow at speed.
The footbeds that they make for you in a ski/boot shop are usually made of cork, foam or a hard plastic. Some of them start at the front of the arch and go back from there (a lot of times, this is what you get if you get footbeds from a Dr), but I would highly recommend full-foot footbeds. The most common are cork Superfeet(brand) footbeds.
They support your arch and the entire bottom of your foot, so that when you stand on your foot, your foot and ankle don't roll in or out. Using footbeds will make your feet warmer and more comfortable because they reduce the pressure points, fill gaps and give space where needed.
I have 3 pair of them. I use one pair to swap between my golf shoes, bike shoes and rollerblades. I have another pair in my snowboard boots and my best pair is in my ski boots. They will last many years, so it's a great investment. The pair I have in my bike shoes is from 1989, and they are still in great shape. You might even be able to get your insurance to pay for it, or at least write them off on your taxes as medical costs (yeah, I know... that whole % of AGI thing...).
In ski boots, they put the entire bottom of your foot in contact with the bottom of the ski boot. That way, when you try to turn your feet and legs, the boot, and therefore, the ski will respond much more precisely and quickly than if your foot is slopping around in there. In general, they will greatly affect your skiing (for the better), not to mention making you more comfortable.