Okay, you're African-American.
Did your parents immigrate recently from Africa? From the Carribbean? Can you trace your lineage back to the days of slavery? Are you "African-American" because you were born in South Africa (like Charilze Theron)?
It could be as simple as, "I am African-American. My family can trace its lineage back to circa 1874 in the area of what is now western North Carolina. Before that is anyone's guess."
In my case, "I am white and Hispanic. My parents came here from Cuba after Castro took over. My paternal grandparents were from Spain, the rest from Cuba."
All you have to do is play with the maximum length.
They're trying to understand who you are and where you come from, not trying to profile you to screw you over. They are seeking a context and framework into which they will begin placing the pieces of your application. It's no different than asking someone you've just met, "So where are you from?"