OK, so now we know that umami has a huge role in worldwide cuisine. It's got a Japanese name, but it's hardly an exclusive Japanese thing. Nevertheless, given the prevalence of umami in Japanese food, it's not terribly surprising that a Japanese scientist first "discovered" umami as a distinct taste phenomenon with a distinct molecular basis. And this was only about 100 years ago, meaning that the "umami" concept is a pretty recent one, even in Japan.
Umami was discovered by Kikunae Ikeda, a chemist at Tokyo Imperial University (today's University of Tokyo, Japan's most elite school). After a contemporary hypothesized that "good taste stimulates digestion" Ikeda was apparently inspired to research the connection between flavor and nutrition. Having grown up eating large amounts of kombu dashi (high-umami broth made from a kind of kelp called kombu in Japan), Ikeda had noticed something unique about dashi. It was mild, yet highly distinctive. It wasn't sweet, salty, sour, or bitter. So Ikeda set out to identify the chemical basis of kombu's flavor.
The Basic Tastes
In order to understand the significance of Ikeda's discovery, we need to understand the concept of "basic tastes." According to Ikeda, "physiologists and psychologists recognize only the four tastes sour, sweet, salty and bitter." He distinguished other apparent "tastes" as being something else: "A hot sensation is just a skin mechanical sensation" and "such qualities as metallic, alkaline and astringent are not considered to be tastes (at least not pure tastes), because they cannot be separated from the sensation accompanied by tissue damage."
Now let's pause for a second and consider that last statement. How does one draw a line around what constitutes a "taste" and what doesn't? Ikeda was writing before we knew a whole lot about cell biology, so we'd like to know how these phenomena are classified by modern scientists. It seems that the five "basic tastes" all are due to interactions of particular chemical compounds with associated chemical receptors in the taste buds.
As a recent article entitled "The Cell Biology of Taste" explains, taste "is the sensory modality generated when chemicals activate oral taste buds and transmit signals to a different region of the brainstem." But the article goes on to state that "[t]aste is commonly confused with flavor, the combined sensory experience of olfaction [smell] and gustation [taste]." It "is also commonly confused with somatosensory sensations such as the cool of menthol or the heat of chili peppers." This latter phenomenon, through which other non-taste nerves in the mouth "are capable of responding to irritative chemical stimulation" is referred to as "chemesthesis." Generally speaking, chemesthetic sensations include (1) chemical irritation and pungency (examples include capsaicin in chili peppers, piperine in black pepper, gingerol in ginger); (2) astringency (examples are tannins and ethanol in wine); and (3) cooling (menthol in mints).
All that said, research on taste is still evolving. For example, "The Cell Biology of Taste" explains that "evidence is mounting that fat may also be detected by taste buds via dedicated receptors," meaning that "fat" may turn out to be a sixth basic taste (fatty flavor has historically been viewed, like chemesthesis, as "somatosensory" in that it derives from a food's texture rather than arising through a gustatory signaling pathway).
The linked articles above, as well as this BBC piece, are really illuminating if you're interested in further reading on taste science and chemesthesis.
A Bit About Evolutionary Biology
So why do we experience these basic tastes in the first place? Why did we develop these complex signaling pathways so that we could experience the tastes of sugars, organic acids (sourness), glutamate, and salt? Professor Ikeda was inspired by the notion that "good taste stimulates digestion." And that notion--that taste sensations send a message to the stomach to prepare for digestion of the kinds of foods being eaten--is tied to the evolutionary history of taste.
Taste evolved not only as a means of stimulating digestion. It also evolved as a way to lead us toward nutritious foods--and away from poisonous ones. One scientist explains it this way: "Among the five tastes, salty, sweet and umami (meaty or savory) are appetitive, driving us toward essential nutrients, whereas bitter and sour are aversive, alerting us to potentially harmful substances." And another pair of authors tells us that each of the various basic tastes "is believed to represent different nutritional or physiological requirements or pose potential dietary hazards."
Sweetness signals the presence of carbohydrates, saltiness signals critical dietary salts, and umami signals protein. Bitterness is described as "innately aversive" and signals the presence of toxic compounds (it's no coincidence that a lot of poisons actually taste bitter). It's probably not a coincidence that our sensitivity to bitter compounds is significantly stronger than our sensitivity to sweet compounds. Sourness is considered "generally aversive," because our bodies want to control the amount of organic acids taken in. That's also why spoiled foods, which contain lots of acids, often have a sour taste.
Adding Umami to the Basic Taste Roster
Let's go back to Ikeda's seminal 1909 paper, entitled "New Seasonings," in which he postulated that "there is one other additional taste which is quite distinct from the four tastes. It is the peculiar taste which we feel as 'umai' [loosely translated as "savory" or "delicious"] arising from fish, meat, and so forth. . . . I propose to call this taste 'umami' for convenience."
Ikeda employed a painstaking series of extractions, chemical separations, and crystallizations to ultimately identify ionic glutamic acid as the source of umami. And when I say "painstaking," I mean it. Ikeda worked in an age before the technological revolution gave us the wide array of powerful analytical instruments we now have at our disposal. The techniques he used are practically a lost art today. An article in the Journal Chemical Senses distills Ikeda's work as follows: it "was done with the procedures of classical chemistry, aqueous extraction, removal of large-scale contaminants  by crystallization, lead precipitation and numerous other steps of preparative chemistry. Finally, low-pressure evaporation resulted in the slow crystallization of a single substance with the mass formula C5H9NO4: glutamic acid."
Reading "New Seasonings," one is struck by the number and variety of steps Ikeda had to undertake in order to take a piece of kelp and reduce it down to pure crystals of the single molecule responsible for umami (actually he took 38,000 grams--about 84 pounds--of dried kelp, and reduced it to 30 grams of glutamate). Getting there must have required a tremendous amount of trial, error, and, above all, patience.
For this achievement, Ikeda has been named one of Japan's "Ten Great Inventors" by the Japanese Patent Office. But Ikeda took it a step further and commercialized his invention. As he explained in his paper, "[a] rational method of production satisfying this natural preference [for umami] must be developed." And so it was. Ikeda obtained a patent on his process and partnered with "Mr. Saburosuke Suzuki, a well-known iodine vendor," and created Ajinomoto, the company that pioneered the commercialization of MSG. If you see MSG in a grocery store today, there's a good chance it's sold by Ajinomoto.