Imagine your boobs feeling so full of milk that you're pretty sure they'll explode at any moment. That's engorgement.
Your first experience with engorgement will probably happen a few (usually two to four) days after delivery. Then your body will switch from producing thick, yellow colostrum to squirting out full-fledged milk. When this first happens (aka when your milk "comes in"), it's normal for your breasts to get swollen, hard, or painful. The hugeness isn't all milk — increased blood flow and swollen tissues (especially if you received IV fluids during childbirth) will contribute. But don't worry — you aren't doomed to heavy, sore breasts for long. The pain generally subsides within 24 to 48 hours. (And some women don't experience engorgement at all.)
The best remedy for engorgement is a hungry baby. If you're feeling uncomfortable, breastfeed as often as every hour or two, and don't be afraid to wake your baby to eat (or to put him to the breast when he's drowsy or in a light sleep). It can also help to massage your breasts as your baby nurses and to briefly apply a cold pack to your breast after nursing. Sometimes engorgement makes it tough for baby to latch on. If this is the case, try pumping (or hand expressing) a little milk before nursing — just to soften things up a bit. And if you just can't handle the pressure, most doctors say it’s okay to take a mild pain reliever, like acetaminophen (Tylenol) or ibuprofen (Advil, Motrin). Check with your doc first.
Baby should be softening at least one of your breasts during each feeding. If 48 hours pass and you're still engorged after feeding baby, try using a pump to completely drain your breasts. If your engorgement isn't relieved, your milk supply could suffer. (Your breasts need to be emptied in order to signal your body to make more milk.)You shouldn't do this more than once every 24 hours unless absolutely necessary, though frequent pumping in the first week can cause you to chronically overproduce milk. Just pump enough to feel comfortable. Later in your breastfeeding adventure, your breasts might become engorged if you skip a few feedings without expressing much milk. If this happens, you can relieve the pain by pumping or nursing. It is important to try to avoid this whole scenario — which can lead to plugged ducts and mastitis — by pumping every three to four hours if you're away from baby and nursing frequently when you aren't.