To extract coordinates from a 3D Plot in Mathematica, the use of the Reap and Sow functions is essential. The provided code snippet demonstrates how to plot a function while simultaneously capturing the coordinates of the points plotted. By utilizing the EvaluationMonitor option with Sow, the coordinates of each point, along with their corresponding function values, can be collected. The final output can be accessed using Reap, which retrieves the stored coordinates. This method effectively allows for the extraction of all plotted points from a 3D visualization in Mathematica.