The centroid is defined as the center of mass of a geometric shape, which can be found by calculating the average of the coordinates of all points in the shape. To find the centroid of the region bounded by the curves y=1/x, y=0, x=1, and x=2, one must first sketch the area to visually estimate its location. The exact coordinates of the centroid can be determined using integral calculus to compute the necessary averages. The discussion emphasizes the importance of defining the centroid before proceeding with calculations. Understanding the boundaries and the shape of the region is crucial for accurate centroid determination.