Carl,
The shape of the pincers varies quite a bit from species to species and even specimen to specimen. The ones on my specimen are a lot longer and thinner, but I'm too short of time right now to shoot and post 'em out. (Besides, Wim's picture is so beautiful, do we really need two of them?)
As far as I have seen personally, the pincers ("forceps") are just for defense. But Wikipedia says "The forceps are used for a variety of purposes. In some species, the forceps have also been observed in use for holding prey, and in copulation. The forceps tend to be more curved in males than in females."
As to why they're called earwigs, I personally prefer the "old wives' tale" explanation that they're thought to crawl into ears.
Wikipedia offers other possibilities.
--Rik