Source and sink flows are illustrated through examples like water pouring from a point and draining into a sloped area, respectively. These concepts are relevant in various applications, including boundary layer flows and the operation of turbines and compressors. The discussion highlights the practical application of these flows in analyzing airflow over aircraft wings, specifically through the vortex panel method. The participants seek clarity on the occurrence of source and sink flows in real-world scenarios beyond simple examples. Overall, the conversation emphasizes the importance of understanding these flows in fluid mechanics.