It could be yeast (aka thrush), a fungus that grows in warm, moist areas such as a baby’s mouth
or diaper area, or on a breastfeeding mother’s nipples. To diagnose it, try gently scraping it off with your fingernail. Leftover milk will come off fairly easily; yeast won’t.
My first-line treatment for yeast is to mix 10 drops of grapefruit-seed extract per ounce of water. Apply this to your baby’s tongue (and, if you’re breastfeeding, to your nipples) every two to three hours for at least a week. If this doesn’t work, see your pediatrician.