To the right you see a flow network with source labeled $s$, sink $t$, and four additional nodes. The flow and capacity is denoted $f/c$. Notice how the network upholds skew symmetry, capacity constraints and flow conservation. The total amount of flow from $s$ to $t$ is 5, which can be easily seen from the fact that the total outgoing flow from $s$ is 5, which is also the incoming flow to $t$. We know that no flow appears or disappears in any of the other nodes.


Below you see the residual network for the given flow. Notice how there is positive capacity on some edges where the original capacity is zero, for example for the edge $(d,c)$. This flow is not a maximal flow. There is available capacity along the paths $(s,a,c,t)$, $(s,a,b,d,t)$ and $(s,a,b,d,c,t)$, which are then the augmenting paths. The capacity of the first path is $min(c(s,a)-f(s,a),\; c(a,c)-f(a,c),\; c(c,t)-f(c,t))\; =\; min(5-3,\; 3-2,\; 2-1)\; =\; min(2,\; 1,\; 1)=1$. The last path does not exist in the original network, but if you send flow along it, you still have a legal flow.

If this is a real network, there might actually be a flow of 2 from $a$ to $b$, and a flow of 1 from $b$ to $a$, but we only maintain the net flow.