They probably don't live in the U.S. @my
For me she came the day after i got home.
And she takes baby's weight, checks for everything from joints being good, the umbilical cord being healthy, they'll take the clamp off so its not as awkward to change baby. They'll give you info, if your breastfeeding they check to see how well baby will latch on. Then for you they take your blood pressure, they check to see if your uterus is good an going to normal. And if your baby didnt get his blood work done in the hospital they do that at the house.
So really its exactly what they do in the hospital