I understand how the last 4x4 matrix is created(the math operations);however I do not understand why the resultant matrix indicates that there is an edge in the image. In the resource it basically says : "If we interpret the matrix on the right as an image, there will be a lighter region (white) in the middle, that corresponds to the vertical edge detected in the center of an original 6×6 image." but it makes no sense for me why lighter region in the middle indicates vertical edge.
If it helps, try a simpler version. Just look at two neighbouring pixels in a row.
First example: There is 10 and 10. Difference between them is 0, no difference, no edge.
Second example: In the middle, there is 10 and 0. Difference is -10 because it drops from 10 to 0. There is a step of -10, that must be an edge.
The 3x3 kernel just takes the source pixel numbers from larger area.
Instead of two adjacent pixels and one row, it takes them from three rows, and there is a gap of one pixel in between horizontally.