It depends! In American English (and British English) "quite + adjective" means "to a large degree." So in the phrase "the person/animal is quite dead" means he/it is definitely, beyond a doubt, dead. But in British English, "quite + adjective" can also mean "not completely." So in the phrase "the person/animal is quite dead" means he/it is not actually dead, but almost dead. Obviously the meaning depends on context and on whether one is using an American expression or a British expression.

Another common usage is "This town is quite dead", meaning it's not very exciting. Often used of a town with no nightlife. Thumbs up for Alan's answer too - for me in Australia, "quite dead" means "definitely dead".