The cream whipper relies on gas expansion to work.
When you make whipped cream by beating, you beat fine air bubbles into the cream. The cream traps air and becomes essentially a matrix that holds those bubbles--a foam.
Your gas-charged whipper does the same thing in a totally different way.
When you charge the whipper with gas, there's high gas pressure inside with the cream. The cream will actually absorb the nitrous oxide you put in. Because of the pressure, the gas absorbed can be thought of as really really really small bubbles within the cream. So you have a matrix of gas and cream, but because the bubbles are so small, it's essentially just cream.
Chilled liquids more easily absorb gases at high pressure, which is why it's good to use cold cream and keep the whole unit in the fridge. A limited amount of agitation (shaking) exposes more cream to the gas, improving absorption.
When you release the cream from the device, the absorbed gas expands rapidly. The bubbles get bigger, and your cream to bubble ratio becomes more like the foam that we know as whipped cream. It's really exactly the same thing, only with nitrous oxide instead of plain ol' boring air inside the bubbles.
Why nitrous oxide? As I understand it, it's because it's the cheapest non-toxic, odorless and tasteless gas you can get. Carbon dioxide would almost be a good choice, but unfortunately it's bitter. Not a good match for cream.
Finally, why is shaking too much a bad thing? That one I don't know for sure, but I know what happens when you over-whip cream with the mixer. You make butter. Perhaps the gas or high pressure encourages this conversion, or maybe you're just churning it that much when you over-shake. Either way, I'm sure you've essentially made butter when you shook it too much.
These soaps are simply soap-shaped lumps of stainless steel. You'd get the same results from rubbing a spoon on your hand, or rubbing your hands on the sink.
There's a ton of anecdotal evidence that stainless steel works; unfortunately there seems to be very little scientific evidence backing it up. I've never read any in the past, nor was I able to find anything convincing while researching this answer.
Various explanations abound but should all be treated as speculation until some hard experimental data comes out:
About.com's Chemistry Ph.D thinks it's a chemical reaction with sulfur, but admits that it's speculation. I find that explanation dubious at best, because the whole point of stainless steel is that it's non-reactive, and not all of the odours that S.S. supposedly removes are based on sulfur.
Another cooking blogger references McGee and postulates that it might be due to static electricity, which is sort of corroborated by the Straight Dope's hypothesis of ionization. Follow-up comments to the former entry dispute his claim, as well.
Finally, the Straight Dope link above also suggests that the metal might simply be acting as an abrasive. This, to me, is the most plausible explanation, but there's still no specific evidence supporting it. Again, if you care about anecdotal evidence, someone did a little experiment on SD's discussion board and claims that rubbing with anything works - it doesn't have to be metal - which supports the abrasive hypotheses. Then again, it's questionable whether the experimenter here actually impregnated the skin or just got a little scent on the surface.
So make of it what you will; nobody seems to know for sure why it works, but anyone who's tried it can tell you that it does work.
But don't waste your money on one of those "metal soaps" - just use a metal ladle, or the handle of a knife, or any other metal surface, and rub it on your hands under cold running water.
Best Answer
From the cuisinart manual parts description section(emphasis mine):
So it looks like you are using it correctly. I am going to have to try using this when adding milk or butter milk to my biscuits.