I must disagree with the below.

Old? definitely. Inaccurate? Ofttimes. Racist? Only if one incorrectly presupposes that the term is used to characterize hypodescent: The assignment of the perceived subordinaterace on a child of mixed lineage.

I'd argue that one should be proud of their African heritage, regardless of the number of grandparents who share it.

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Saying that a person has 1/16th African blood is an old, inaccurate, and sometimes racist way of saying that one great-great-grandparent was African and the other 15 great-great-grandparents were from some other racial group.

It can also mean that two great-great-great grandparents, who were not married to each other, were African; or that four great-great-great-great grandparents not married to each other were African, etc., etc.