This is the what the
South African people call
Nelson Rolihlahla Mandela. It is a
term of endearment which has become widely used when referring to the
most famous political prisoner of all time.
The reason he became known as Madiba, is that this is his clan name, ie: he comes from the Madiba clan, a very well-known clan in the Eastern Cape of South Africa.
The first people to call Mr. Mandela 'Madiba' were his fellow prisoners on Robben Island. In order to refer to each other in a sort of code which the guards would not understand, the prisoners used each others' clan names. Apparently most of them had a whole series of these clan names as the names serially represent your father's name, your grandfather's name etc.
When he was released from jail, the South African public (many of whom did not know what Nelson Mandela looked like because of the stringent press ban on publishing photographs of him or any likeness of him at all) adopted this name for him and we all know him as Madiba now.