I have two Cylinders. To the first I apply a Subdivison Surface Modifier first (see the right object in the picture). Then I create a second object (cylinder left) and apply the Boolean Difference Modifier. The result is not a hole as I expected. How to cut a perfect round hole?
It looks from the screenshot that you don't have an object selected. This, in and of itself, is an odd behavior, as nothing at all should be happening, but it may possibly fix itself as you continue. Click on the orange cube in the Boolean Modifier (a list should pop down) and select the other object, or click on the eyedropper and select the other object that way.
As a note, no aspersion intended on rob, I'm certain it was a mistake, when applying modifiers, you apply from the bottom of the list upwards. CLARIFICATION: Whatever order modifiers appear, they should be applied in the order they're affecting the object. First in, first out.