To "have" a child means to give birth. This can be a little confusing because to "have a child" also simply means that you are a parent and your son or daughter exists. But you usually use "have" in the present tense to mean that you are a parent:
I have a son.
She has three daughters.
And you use "had" in the past tense to mean that you gave birth to a child:
I heard she just had a baby.
But there is also a case where you use the past tense to mean that someone did have a child, but now the child or the parent is dead:
Mark Twain had four children.
We had a son, too, but he died soon after birth.