This lecture provides a detailed example of the Ford-Fulkerson algorithm using a residual graph to find the maximum flow from a source to a sink in a given graph. The instructor explains the process step by step, starting with an initial flow of zero and iteratively finding augmenting paths to increase the flow. The lecture demonstrates how to update the residual graph after each iteration, push flow through the augmenting paths, and determine when the algorithm reaches the maximum flow. The instructor emphasizes the importance of choosing augmenting paths strategically to optimize the algorithm's performance and efficiency.