This is what Wikipedia has to say about it:

In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Hera's breast while she is asleep so the baby will drink her divine milk and become immortal. Hera wakes up while breastfeeding and then realizes she is nursing an unknown baby: she pushes the baby away, some of her milk spills, and it produces the band of light known as the Milky Way. In another Greek story, the abandoned Heracles is given by Athena to Hera for feeding, but Heracles' forcefulness causes Hera to rip him from her breast in pain.

That Zeus. He’s such a character. Not only does he sleep around on Hera (you know, his ~~sister~~ wife), but then surreptitiously tries to get Hera to breast-feed his bastard son. But I digress…

I feel this deserves more attention. Not only is the Milky Way named for literal milk; it is named for specifically for human milk.