Well Maybe the dragonfly photo was taken with a lens opened up with a large aperture to give a very small depth of field. To Blur the background if it hasn't been blurred you can copy the background layer to a new layer. Then you have two options:
1.) In the copied layer, select the foreground object and delete the rest. Then select the background layer and blur it.
or
2.) Blur the copied layer and apply a layer mask to the copied layer and mask out the foreground with black.
Gaussian or Lens blur are the blur filters that I would probably use.