Etymology: the word comes to English via the Spanish cebiche (fish stew), but the origin of that word is disputed. One suggestion is that it is derived from the Spanish escabeche (pickle). Another suggested origin is a Spanish-Arabic word meaning "meat cooked in vinegar". Another potential origin is siwichi, the Quechua word for the dish (I think it means "tender fish"). It looks like its common use in North American English did not begin until sometime in the 1980s.
Part of the reason for the dispute over the name of the dish is that the origin of the dish itself is unclear. The current theory seems to be that the dish originated in Peru, as a variation on a dish brought there by Moorish women from Granada, who traveled to Peru with the Spaniards.
However, the basic concept of marinated raw fish was common in South America before the Spanish conquistadors: the Moche people marinated their fish in fermented banana passionfruit juice, and the Incas used chicha (a slightly fermented beverage made from corn). When Old World explorers arrived, they brought citrus fruits.
The acidic marinade does not actually cook the seafood. But, like cooking, it denatures the proteins, causing the fish to become firm and opaque. As with cooking, marinating the seafood too long can make it rubbery.
As with sushi, good ceviche can be wonderful, but bad ingredients can make for a terrible experience. Cooking (or sufficient freezing) can kill most fish parasites, but the acidic marinade in ceviche will not. And neither cooking nor freezing will alter most fish toxins (the causes of seafood poisoning). So the quality of the fish is important: if you're not willing to eat it raw, then you shouldn't eat it in ceviche.