Ambrosia is a word that names its own effect. It means, at bottom, "not mortal."
Etymonline traces it to Greek ambrosia, a noun made from ambrosios, "divine." That adjective probably meant "of the immortals," from ambrotos, "immortal, imperishable." Split it open and you find the negative a- and mbrotos, a form related to the word for "mortal." The root behind it, Indo-European mer-, produced words for dying and death across the family.
Sanskrit has a near twin. Amrita, the drink of immortality in Hindu myth, combines a-, "not," with a word for death. Wikipedia notes that both words appear to come from one reconstructed form meaning "un-dying." In one famous story, gods and demons churn the ocean together to bring up a pitcher of amrita, then fight over it. The parallel suggests the idea of a deathless food is older than Greek or Sanskrit.
In Greek poetry ambrosia was more than a meal. Homer usually makes nectar the gods' drink and ambrosia their food. Other poets swapped them: Alcman made nectar the food, while Sappho made ambrosia a drink. In the Odyssey, doves carry ambrosia to Zeus. In the Iliad, Hera cleanses her body with it, and Apollo anoints the corpse of Sarpedon. It worked as food, perfume and preservative at once.
Mortals were not supposed to have it. Britannica notes that in Pindar's first Olympian ode, Tantalus stole nectar and ambrosia from heaven and gave them to mortals. It was one of the crimes for which he was punished.
English borrowed the word through Latin in the 1560s, for the food or drink of the gods. By the 1680s it was being used for foods humans could actually eat, originally fruit drinks. By 1731, Etymonline says, it meant anything delightful.
The word also gave English a first name. Ambrose comes from Latin Ambrosius, from the same Greek ambrosios. Saint Ambrose, the fourth-century bishop of Milan, carried a name that meant "immortal."