What is the Use of the Opening Operator
Opening is the morphological operation used for example in removal of small particles or some noise in binary image. Additionally it is widely used in hand-writing recognition where you want only the 'skeleton' of your letter.

Mathematically it is a dilation of the erosion. Erosion sets current pixel to 0 if any pixel in neighbourhood is 0. Dilation on the other hand sets pixel to 1 if any neighbour is 1. 

You can think of that in following way: first you do the erosion ($N$ steps), which is shrinking boundaries of your objects. After that you perform dilation (also $N$ steps), which is expanding boundaries of your objects. Because small ones were removed in erosion step you will bring back biggest elements. 

Here is some image showing this operation: