For what are Georg and Ulrich fighting?

Besides the obvious reason that underlies the feud between Ulrich von Gradwitz and Georg Znaeym, which the other response eloquently describes for you, one could argue that the real reason for their feud goes deeper than a land dispute.
Both men are the patriarchs of their families, and both men feel responsible as the leader of their clans to make the right choices in the families’ best interests. For each, this means claiming the disputed tract of land for his family. Is this land really any better than a similar tract that the Znaeyms’ could obtain? Do the Gradwitz' honestly need the small patch of land? The answer to both of these questions is a resounding no.
Therefore, it becomes clear that the land is not what is most important here. Rather, each man wants to demonstrate his prowess and superiority over the other, proving to himself and his family that he “wins.” This dispute is more about male ego and dominance than the land dispute they use as an excuse to feud, which is why Saki’s ending is darkly humorous. In the end, it takes death for these relentless, misguided men to finally quash their quarrel.

Ulrich von Gradwitz and Georg Znaeym are engaged in a territorial dispute over a narrow strip of steep woodland, which is technically owned by the Gradwitz family. The dispute between the two families has lasted for three generations and stems from the Znaeym family's refusal to acknowledge the court's decision to grant the land to the Gradwitz family. The territorial dispute between the two neighbors is known throughout town and becomes personal between Ulrich and Georg. Both men accuse the other of illegally poaching on their territory, and the ill will between their families has been passed down to their sons.
At the start of the story, Ulrich is wandering through the steep slopes of the disputed territory in hopes of finding Georg and killing him. However, both men meet face-to-face, and a massive tree falls on them before either man can harm the other. While stuck underneath the fallen tree, the two men reconcile their differences and become friends before they are devoured by wolves.