The residual graph shows remaining capacity after you have assigned some flow. For each edge (u,v) with flow f(u,v) and capacity c(u,v), the residual graph has:
1. Forward edge (u,v) with capacity c(u,v)−f(u,v) (remaining capacity).
2. Backward edge (v,u) with capacity f(u,v) (allows you to undo flow).
The backward edge is the core concept. It lets you reroute flow if you find a better path later. This is what makes flow algorithms work.