It is referred to as farrowing as another name for piglets is farrow.
Parturition, or the act of giving birth.
In horses, parturition(the birthing process) is often called "Droping the foal."
Calving.
A young female pig (swine) is referred to as a "gilt" - until after her first pregnancy (or litter of pigs/piglets). After giving birth (parturition) from her first pregnancy, a female pig (swine) is thereafter referred to as a "sow".
Parturition
childbirth
Parturition
Whelping or parturition.
parturition labor
Calving, or giving birth.
Young swine are called piglets.
A swine offspring is called a piglet.