The structuring element tells the operation which pixels it is supposed to act upon and which pixels it is supposed to ignore. For example if you're doing a dilation, and your structuring element is
0 1 0
1 1 1
0 1 0
Then it will look only at those pixels in the "+" shape when deciding which of them is the maximum (which is what a dilation is). A closing is a dilation followed by an erosion (local minimum) and has the effect of closing up little nooks and crannies in your binary image, or of expanding out bright areas in your gray scale image.
