If something is patronymic, it comes from your father's name, or perhaps the name of one of his ancestors. Last names like "Wilson" and "Johnson" are patronymic.
In some countries, patronymic names are extremely common. Take Iceland, for example: instead of having a last name that can be traced back generations through their father's family tree, most Icelanders' last names reflect their father's first name followed by "son" (or occasionally their mother's first name followed by dóttir or "daughter"). If your father's name was Jón Kárason, instead of sharing that last name, your last name would be the patronymic Jónson, or "son of Jón."