This very old saying means that, ultimately, family ties are more important than anything else. "Family" here means blood or genetic relatives, not in-laws or even husbands and wives; certainly not friends, however much loved. The idea is that, in the last analysis, the only people you can really rely on, and the people to whom you always have a duty no matter what, are those with whom you share a genetic inheritance. (If you're in business, your relatives may well use this saying to try and get a discount!)
Today the saying is still in use, although in many ways we probably think less in terms of blood relationship than we used to, and more in terms of what role a person has played in our lives. To give one example, it is quite common for children to regard a stepfather, if he has lived with them for most of their lives, as more their "real" father than their biological one. At the same time, people still do attach great importance to the blood tie, as is shown by the number of adopted children who try to make contact with their birth parents, for instance.
Today the saying is still in use, although in many ways we probably think less in terms of blood relationship than we used to, and more in terms of what role a person has played in our lives. To give one example, it is quite common for children to regard a stepfather, if he has lived with them for most of their lives, as more their "real" father than their biological one. At the same time, people still do attach great importance to the blood tie, as is shown by the number of adopted children who try to make contact with their birth parents, for instance.