You cannot change a leopards spots, is a British saying, (click to understand what is meant by English, British and UK), used to describe someone who will not change.

It is usually used when some one is doing something wrong, unethical, unreasonable, to others or their surroundings. 

A leopard has a coat of fur which has many spots, and these spots never change throughout its' life.

                                                                    

Therefore, when this saying is used towards another person who is doing something we do not like or is wrong, it means that they will not stop doing it, will continue doing it now and in future events. 

When someone is saying or doing something, an observer may say a leopard never changes his spots, this is enough for a listener to understand who the saying is directed towards.