The answer to this can be found at the start of Chapter 6. The two groups were the Genoese (from Genoa in what is now Italy) and the Mongols.
Kaffa was located in the Crimea in what is now Ukraine. It was a very important site, Bernstein says, because it was located at the end of the Silk Road. It was, therefore, a major trading site at which goods from Europe were exchanged for those from the East. Because the city was so valuable, the Mongols and the Genoese both wanted control of it and they struggled for in during the early 1300s.