Many countries that put patronymics into practice have used the system for thousands of years. The given names were so common that it was a way in which they could more specifically identify an individual. The name Jens Hansen is like saying "Jens, son of Hans," or Klaas Jansen, "Klaas, son of Jan." There may have been more than one person of the same name even with patronymics, but at least it was a start.
Many find the Scandinavian and Dutch form of the system confusing, but by taking the name and dividing it into two parts, patronymics become easy and helpful in doing genealogical research. The first part of the name is the father's given name, which is followed by a form of the word for son or daughter in the native language as the second part.
Another aspect of the patronymic surname that may be helpful when researching in some parts of the world is that it can be easy to determine the gender of the child based on the surname given, if you are unable to determine it from record headings or the given name itself. This is especially helpful when a person is unfamiliar with given names of a country and the gender with which they are usually identified. Parish priests were not required to follow guidelines when recording names, so it is important to be careful when establishing the gender according to surname endings even before that time.
Any time you have a patronymic surname, you already have the first name of the person's father if they were legitimate, which is very helpful. Even if the child was illegitimate, some Scandinavian parish priests still recorded the name of both parents, so that problem is solved.
Most countries have ended the use of patronymics, requiring families to take a surname that is then passed on. In some countries where the government has stopped patronymic use, it is still possible to find the system continue on for another decade. During the transition period of Scandinavian countries, it is not uncommon to find given name, patronymic, and then the father's patronymic surname for a person in the records.