Carat is a term that describes the purity of gold. 24 carat gold is pure gold without any other metal mixed with it. When Jesse Owens says that he felt 24-carat friendship for Luz Long, he means that Long’s friendship was pure and true. When Luz was congratulating him after winning the gold in the board jump finals, it was not the fake smile with a broken heart, but a genuine one. Luz was genuinely happy that his friend Owens won the gold medal. 
 
The ‘real friendship’ between them was formed when Jesse met Luz in his quarter to thank him for helping him out and they talked for two long hours about sports, about themselves and a dozen other things.