The main conflict of the story is between two families. A little context is necessary to understand what is going on. In the short story, there are two families that have been feuding over a strip of forest for decades. The courts ruled in the Gradwitz family's favour but the Znaeym family never accepted this.
This quote will give you the whole story in short:
A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners; the dispossessed party had never acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations. The neighbour feud had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to it was Georg Znaeym, the inheritor of the quarrel and the tireless game-snatcher and raider of the disputed border-forest.
What makes the conflict in the story more intense is Ulrich is wandering through the woods and he comes in contact with Georg. They both are armed and ready to use it on each other. But at this moment, there is a blast of wind and a tree happens to fall on them. Both men are pinned down and cannot use their weapons against each other. Here they have to face each other until help comes. Both men hope that someone from their camp will come. Even in the face of possible death, conflict remains.
However, as time progresses, their humanity comes out and they begin to reconcile. When they hear footsteps, they are ready to make amends. The irony is that the steps are the steps of wolves.
The conflict then is between two family, and in particular, between two heads of families.