Breast suckling stimulates production of oxytocin, hormone responsible for milk flow and its movement in milk ducts.
Oxytocin stimulates contractions of smooth muscles surrounding lactiferous alveoli and ducts, and they make the milk flows out. The contractions can be felt as tingling, stinging, hardening or tension in breasts. Some women like this feeling, while others consider it unpleasant or even painful. There are also women who do not feel any oxytocin spasm (also called a letdown reflex).
The oxytocin spasm occurs after a few or several seconds from the breastfeeding start, and passes quickly. It can be stimulated not only by the baby's suckling, but the very sight of the baby, his crying, or even by thinking about breastfeeding or the baby. The breast tenses and milk flows out (not always).
What you can do
You do not have to do anything. The oxytocin spasm is a natural and necessary component of breastfeeding, as without oxytocin milk would not flow. How you feel your oxytocin contraction is an individual feature of your lactation. Usually, it is most strongly felt when breasts are overfilled. That is why it causes stronger pain in the breasts with milk stasis or mastitis, as well as during excessive milk production. Here you can read how to cope with those situations: Milk stasis, Mastitis, Milk flowing too fast, Breast fullness.