I take it as a metaphor to indicate that many people are needed to raise a child. Parents can do it all on their own, but that puts a lot of pressure on the parents and it leaves the children without any other resources to rely on. To keep parents sane and to make sure the kids can learn how to work with others, we need to conceive of ourselves as part of a network of people; as part of a village.
Who are the babysitters? The teachers? The doctors? Etc. Etc. There is a whole village, and they all cooperate in raising the child and keeping him or her healthy, or learned, or cared for when the parents need some time on their own.
We all cooperate – even strangers, to help each other’s kids. You see a kid on the street, clearly skipping school and looking for trouble, and you tell them then should go back to school. They might not obey you, but it will have an impact. We are all responsible for everyone else’s kids. If we don’t behave that way, civil society will gradually erode.