Literally: ruler/mister – child – leopard – change
Alternately: Originally: a wise person changes with changing circumstances; a wise person is quick to recognize their errors and change for the better. In modern usage, the phrase has taken on an ironic meaning, suggesting that someone clever would change, or has changed, their actions or professed beliefs to match whatever was convenient, profitable, or popular at the moment, without caring for loyalty, consistency, or scruples. The good meaning, then, is adaptability, while the bad meaning is flip-flopping.
君子 (kunshi) is a wise or virtuous person – possibly originally meaning a highly-ranked person, with the value judgments being attached later as the aristocracy decided that they were just the best. 豹変 (hyouhen) describes the seasonal shedding and coloration change undergone by some species of leopard – at least, the Amur Leopard, with a habitat covering the Korean peninsula and areas of Siberia and China, whose summer coat is described as being brighter and more vivid.
This saying is thought to be derived from the I Ching, and is associated with the 革 (animal hide / revolution) hexagram.
Some non-yojijukugo variations exist, including contraction to just the final two characters, or adding す or する (su or suru, “to do”) to the end.
Note that despite a similarity in the image used, this saying stands in no relationship at all – neither synonymous nor opposed – to the English adage “A leopard can’t change its spots.”