Jonas's father is a caregiver at the daycare center. His official title is Nurturer. So his job is, essentially, to take care of the kids. According to the book, his job is to take care of the kids' physical and emotional needs during this earlies stage of their lives.
We know that the kids are given to the families when they are one year old. So Jonas's father and the other workers at the center are only caring for the very youngest kids.
We also know that, at least sometimes, it is his job to release the smaller of two twins.
In the book The Giver Jonas' father was a nurturer. A nurturer works in the nursery with the babies who are under a year old. He had been put on the night shift which he did not like because there was more prestige in being on the day shift.
Jonas' father liked what he did. He also is given the task of putting the children to death who are born imperfect or when a twin is born, he has to eliminate the smallest of the twins.
Jonas' father is a man who brings home Gabriel because he wants to help him to do better. Gabriel has trouble sleeping and if he does not start to sleep nights, he will have to be put to release/death.