Dumbledore makes this remark to Harry in Chapter 17, when Harry is in the hospital, in reference to the imminent death of Nicolas Flamel, Dumbledore’s old partner and inventor of the Sorcerer’s Stone. When Dumbledore announces that he and Flamel have decided to thwart Voldemort by destroying the stone, and with it the possibility of attaining eternal life, Harry realizes that Flamel will die. Flamel is effectively sacrificing himself for the good of Hogwarts and of the world, just as Jesus Christ, according to Christian belief, was supposed to have sacrificed himself for the salvation of humankind. Flamel’s decision reveals his wisdom, all the more so as Dumbledore’s words echo the thoughts of innumerable philosophers and religious figures (from the Greek Socrates to the Indian Buddha) who have similarly seen death as a beginning rather than an end.
Dumbledore’s and Flamel’s wisdom is precisely what is lacking in a villain like Voldemort, who clings unnaturally to life, refusing to accept the natural human adventure of death. By saying that a healthy acceptance of death is a characteristic of a “well-organized mind,” Dumbledore is implying that Voldemort’s manic pursuit of immortality is not well organized at all, despite all of his savvy tricks, but is rather deranged.