|From Gray's Anatomy|
The breast contains mammary glands that produce milk based on hormonal triggers. Some of these hormones are produced in response to suckling - so as a baby nurses the breasts are stimulated to produce more milk. The breasts don't store milk, which is why some moms leak from their breasts.
Human milk contains proteins (including lactose) and fats.
Mammary glands are modified sweat glands. The consist of pockets that drain into the lactiferous duct at the nipple. These pockets, or alveoli, are lined with cells that secrete the fluid we call milk. The pockets become enlarged as milk is produced. Another organ that contains alveoli is the lungs, though they are filled with air and mucus instead of milk.