Borsch is a soup of Ukranian origin that can be served hot or cold. The main ingredient in this soup is beets, but hot borsch is a hearty dish made with beef or pork broth and heavy, starchy vegetables such as potatoes accompany the beets. It is usually served with dark rye bread and is usually served as an appetizer.
Zaroff's having this borsch, "the rich, red soup with sour cream so dear to Russian palates" prior to the entree of filet mignon indicates his strong ethnic traits as well as his hearty appetite. This meal is significant to the character of Zaroff because it suggests a strong, perhaps overpowering and, possibly, brutal nature that is often stereotypical of Russians. Also, since he has red meat, his hearty appetite is further suggested; he may well have other appetites, then.
Interestingly, Connell published his short story in 1924, not long after the Bolshevik Revolution, during which many a peasant starved. As one of the "noble Russians," an officer of the Czar, Zaroff has fled the country. Now, he enjoys his borsch and filet mignon, but he probably feels resentment toward those beneath him who have effected the death of the Czar. Nevertheless, because he "had invested heavily" he enjoys a privileged life and lives in an world imitative of his Old Russia.
In Richard Connell's "The Most Dangerous Game," Rainsford recognizes that General Zaroff is eating borscht when he meets him. Specifically, Rainsford says the following:
"They were eating borscht, the rich red soup with sour cream so dear to Russian palates."
Not only does the soup give Rainsford a hint at Zaroff's Eastern European background, but it can also be symbolic for two other possible reasons. First, the soup itself carries with it both sweet and sour flavors. One might say that General Zaroff is like the soup because he is both sweet and sour. Rainsford describes him as follows:
"He was finding the general a most thoughtful and affable host, a true cosmopolite."
This passage describes the sweet side of General Zaroff. He treats his guests with the best he has to offer. For example, Rainsford is also treated to champagne, fresh pajamas for the night, and an excellent bed and room. However, the sour part comes in when Zaroff's guests are not allowed to leave the island without being hunted down like quarry first. Unfortunately, it seems as though no guest has ever been able to leave the island.
The second way that borscht can be considered symbolic is because some people eat it as part as a religious ritual. For instance, ethnic groups such as Eastern European Jews, or those associated with the Eastern Orthodox church, eat borscht in the context of a religious ritual. Hunting, for Zaroff, is like a religion to him. Therefore, it would make sense that he might eat this favorite dish to commemorate a successful hunt. On the other hand, he might also eat it before an upcoming hunt. In fact, he does ask Rainsford to accompany him on that night's hunt; so it is possible that he eats borscht before he hunts men, as though it might be a good luck ritual.