Answer: I have concluded that Mandela intended the expression 'a rainbow nation at peace with itself and the world' to mean the unity of multi-culturalism and the coming-together of people of many different nations, in a country once recognized with the division of white and black under the Apartheid rule.
Here is a short excerpt from text that might help you further; The phrase was elaborated upon by President Nelson Mandela in his first month of office, when he proclaimed: "Each of us is as intimately attached to the soil of this beautiful country as are the famous jacaranda trees of Pretoria and the mimosa trees of the bushveld – a rainbow nation at peace with itself and the world.
Explanation: Hope this helps! Have a terrific day! <3