Either the baby is not positioned and latched properly, or the baby is not suckling properly, or both.
Incidentally, babies learn to suck properly by getting milk from the breast when they are latched on well. (They learn by doing). Fungal infection (due to Candida albicans), may also cause sore nipples. The soreness caused by poor latching and ineffective suckle hurts most as you latch the baby on and usually improves as the baby nurses. The pain from the fungal infection goes on throughout the feed and may continue even after the feed is over. Women describe knifelike pain from the first two causes. The pain of the fungal infection is often described as burning, but may not have this character. Sudden, unexplained onset of nipple pain when feedings had previously been painless is a tipoff that the pain may be due to a yeast infection, but the pain may come on gradually or may be superimposed on pain due to other causes. Cracks may be due to a yeast infection.
Proper Positioning and Latching
It is not uncommon for women to experience difficulty positioning and latching the baby on. Proper positioning facilitates a good latch and good latching reduces the baby's chances of becoming "gassy", and also allows the baby to control the flow of milk. Thus, poor latching may also result in the baby not gaining adequately, or feeding frequently, or being colicky (topic #3 "Colic in the Breastfed Baby").
Positioning
For the purposes of explanation, let us assume that you are feeding on the left breast.
Good positioning facilitates a good latch. A lot of what follows under latching comes automatically if the baby is well positioned in the first place.
At first, it may be easiest to use the cross cradle hold to position your baby for latching on. Hold the baby in your right arm, the web between your thumb and index finger behind the nape of his neck (not behind his head) with your fingers (except for the thumb) supporting the baby's face from underneath, and your forearm supporting his back and buttocks. Hold the baby's buttocks between your chest and your forearm—this should give you good control. The baby should be almost horizontal across your body and should be turned so that his chest, belly and thighs are against you with a slight tilt so the baby can look at you. Hold the breast with your left hand, with the thumb on top and the other fingers underneath, fairly far back from the nipple and areola.
The baby should be approaching the breast with the head just slightly tilted backwards. The nipple then automatically points to the roof of the baby's mouth.
