Wasabi (わさび) comes from a plant in the cabbage family, closely related to horseradish. Most casual sushi fans have never encountered it! That's because in most of the world a mixture of horseradish powder is used in sushi bars. It comes in large bags with coloring added and is prepared by simply mixing with enough water to get the consistency desired.
Ironically, because of the difficulty of growing it commercially in centuries past sashimi was eaten with mustard - not unlike the so-called wasabi paste we apply today.
The real wasabi plant grows in cool, wet, shady places and until very recently was grown exclusively along shady riverbeds in Japan. The wasabi plant's rhizome is harvested and sent to the sushi restaurants where it can be ground fresh for maximum flavor. The chef grinds it on a ceramic (or soemtimes metal) oroshigane in most sushi restaurants, but traditionally wasabi was ground on a piece of rough shark skin (鮫皮)
Wasabi has a stronger flavor than the artificial paste, but it degrades quickly so freshness is crucial for maximum enjoyment. Freshly ground wasabi should not be mixed into soy sauce, because that only quickens the chemical decomposition of the wasabi. There are sushi restaurants that will serve fresh wasabi, but they will often charge extra for it.
Proper sushi ediquette holds that the itamae will use his judgement and apply a suitable amount of wasabi to each piece of nigiri, if the topping is seafood. It is placed on the underside of the fish before combining with the rice. The amount of wasabi used is dictated by the fattiness or oiliness of the fish, and by the customer's observed taste preferences. But sushi should be enjoyed - feel free to add a little more to suit your taste.
This video clip shows a small scale wasabi farming operation in the mountains of Japan. This farmer has picked a nice cool location by a stream which irrigates his crop. This is not big agribusiness; Japan imports a lot of wasabi every year fromm China and elsewhere.
The wasabi's zing is due to it's natural defense against hungry predators. When animals or insects try to consume the wasabi plant, the chemicals in the plant are mixed, creating a mustard oil. As the oil disintegrates it produces a gas, not unlike mustard gas used in combat, that is a strong irritant.
Wasabi, contrary to popular belief, does not kill the bacteria in the fish that is being consumed. It may, however, aid in digestion and inhibit the growth of bacteria, and thus be a useful additive.
This same chemical reaction is initiated when your local sushi chef grinds the root of the raw plant to create the wasabi paste. Each order should be freshly ground shortly before eating for the maximum flavor because that same chemical process continues after the initial grinding.