Motivation is key, of course. However, I've seen many articles projecting politics on this victory, claiming that the South African players were superior to the English because we played in the name of diversity and acceptance and to give hope to South African race relations, while the English played for Brexit and such. and were psychologically traumatized by the effect the "evil" nationalistic Tory party has on British society. Utter nonsense. It's just a game. Players play for the glory of their nation but also for individual achievement. Just like people working in a diverse office environment, Rugby players have to leave their politics at home or get sacked, hence they create an impression of racial harmony that won't apply accross all of South African society. Most of South Africa is already as unified as a hyper diverse country could ever hope to be and this victory won't change much. If we want any more unity we'll have to actually eradicate our diversity by killing languages, cultures, force mixed relationships to homogenize the future generations, etc. but that will create far too much resistance and even open conflict.
Anyway, we won because we had superior players, a good strategy, a country that takes rugby very seriously for the most part and the had motivation. Our team has had a bed few years so there was a strong desire to show that we are one of the top teams, if not THE top team once again.