Here's how this works: Go back along your family tree until you reach the first immigrant. That is, the first person who eventually settled in a country other than the one they were born in, regardless of country (i.e. this is not intended to be US-immigrant-centric).
Choose only the one answer which corresponds to the most recent immigration. So, for example, if your father is the 3rd generation since immigration but your mother is, herself, an immigrant you would choose "1 generation". The hypothesis we're testing is that the sort of entrepreneurial, adventure-seeking personality that is overrepresented on HN correlates with a willingness to pick up and leave your comfort zone completely.