The drop shadow effect is actually a drawing effect that looks like the shadow of an object.
You can see in the image below how a drop shadow effect appears:
From left to right, the spreading is increased making it more obvious for the drop shadow to appear.
For Paint.Net, you will need an effects pack in order to add one like you see above.
Download effects pack: http://users.telenet.be/krisvandermotten/Downloads/PaintDotNetEffects.html
To add drop shadow, go to Effects -> Object -> Drop Shadow.
