... also known as Mammes, Mammas, Mammet, Mamante, Mames, and Mamede.
Oddly enough, even though in Italy he is especially venerated by women who have given birth in hopes that they will lactate abundantly, his name seems to predate the word mammary. Dictionary.com suggests that mammary first showed up in English in 1682, derived from the French mammaire, which in turn came from the Latin mamma, referring to the mother's breast. Saint Mamas doesn't seem to be linked to breasts anywhere but Italy, even though he is widely venerated in Greece, Spain, Cyprus, and especially Lebanon.
The son of Christian martyrs (Theodotus and Rufina), he was raised by a rich widow named Ammia. She died when he was fifteen, and he soon fell afoul of the governor of Caesarea, an active Christian-hunter. There are many stories about him, but nearly all involve torture, lions, and martyrdom at a young age.
In some stories, he was tossed to the lions following his torture, but the lions refused to devour him and instead guarded him from the executioners. In others, he was being hounded by tax collectors, but slipped from his hermitage to the wilderness, where he stopped a lion from killing a lamb. The lion stayed with him; in fact he rode it into town and was granted exemption from taxation on the basis of... well, lion-riding, I guess.
If you have just delivered a baby, or you are about to, you can present some bread and cheese to him at an altar, pray for a while, and then offer the bread and cheese to the first person you meet in the street. Milk is like bread for babies; thus, the offering is intended to promote lactation.