Vocabulary - Residual Graph

The residual graph shows how much capacity remains after assigning some flow. For each edge with flow $f$ and capacity $c$, the residual graph has a forward edge with capacity $c - f$ and a backward edge with capacity $f$.

The backward edge allows you to undo flow if needed. This is what makes the algorithm work. You update the residual graph after each augmentation. The algorithm searches for paths in this graph.