Banks lend consumers money and charge them interest on that money*.
They are only allowed to charge a set amount of interest for different types of accounts. The rate they can charge their clients is limited by the National Credit Act and regulations and is linked to the Repo Rate.
When the rate goes up, those who owe the banks and other credit providers money have to pay more interest on their debts. When it comes down, consumers get to pay less towards the interest portion of their loans.
This is why the recent increase makes life hard for those with large or many debts.