In my part of the U.S. (Oklahoma) it means your ancestors were mixed Native American. I have no Dutch ancestors at all. Basically to avoid the stigma of being Indian in the late 1800s/early 1900s they said they were "Black Dutch" instead. The story was that they were Dutch but from a family that was the offspring of a Spanish and Dutch person from a Spanish-Dutch war I can't think of.

Source: I'm 1/5th Black Dutch!