For example if you want to draw a square with a pen, you put your pen where the square is, draw the outlines, than fill it up, with a shader, for each pixel, you look at where you are, calculate where the pixel is relative to the square, and output the fill color if it is inside the square. If you want to draw another square to the right, with the pen, you move your pen to the right, but with the shader, you move the reference coordinates to the left. Another way to see it is that you don't manipulate objects, you manipulate the space around the objects.
Vertex shaders are more natural as the output is the position of your triangles, like the position of your pen should you be drawing on paper.