"When pigs fly" is an adynaton, a way of saying that something will never happen.

Adynaton was a widespread literary and rhetorical device during the Classical Period.

As a matter of fact, the whole song "As" by Stevie Wonder is one big adynaton.

Ronald Grambo, Adynaton Symbols in Proverbs.

The implication of such a phrase is that the circumstances in question (the adynaton, and the circumstances to which the adynaton is being applied) will never occur.

The term appears to have originated in the early 19th century United States (particularly in the phrase "pull oneself over a fence by one's bootstraps"), to mean an absurdly impossible action, an adynaton.