The Roman satirist Juvenal used a rare bird, like a black swan, as an image of impossibility, and the comparison entered European languages as a standard figure of speech for the non-existent. It rested on a limited sample: every swan known to Europe was white.
In January 1697 a Dutch expedition under Willem de Vlamingh sailed into a river in what is now Western Australia and found black swans there in numbers. The river was named the Swan for them. The birds were real, common in their own range, and had simply never been within European view.
The phrase then flipped meaning, coming to describe a rare event that overturns an assumption built on incomplete observation. What the birds themselves illustrate is a genuine sampling problem rather than a statistical law, and the popular use of the term for any surprising event drifts well beyond that original point about the limits of inductive evidence.