
Photoshop
This effect (with the blurring known as bokeh) is used quite commonly in portrait Photography as well as wildlife photography and helps to increase the prominence of the object of interest within the image while minimising the distracting effect of the background.
Most cameras have a portrait setting which will help to achieve this effect. They do this by maximising the aperture size of the camera lens (letting in more light) which in turn has the effect of minimising the depth of field (a term used to describe how much of the image in front and behind the object of interest is in focus, the smaller the depth of field, the smaller this distance and the more blurred the foreground and background will be - the Wikipedia page on bokeh linked to below has some very good examples of this) so that when you focus on the point of interest, the fore and background will be blurred.
If you have an SLR camera (one with a detachable lens) you can manually achieve the same effect by maximising the aperture (i.e. setting the lowest f-stop number possible). You can usually do this by setting the camera to manual or aperture priority mode (which will let you alter the aperture size yourself, rather than the camera choosing a value).
Other techniques you can use to maximise this effect are to ensure that the object of interest is as far away from the background as possible (may be impossible with wildlife photos, but you can always ask people in a portrait to move!).
The effect can be further emphasised by setting the camera to the highest zoom possible while standing as close to the object of interest as possible.
Another option is to "cheat" and use image editing software such as
Photoshop to apply a "blur" filter to your image background although this does not achieve quite the same effect as that produced by a camera as the blurring will be uniform across the background whereas in a real photo the blurring will vary depending on the distance of the background object from the point of focus.
For more information please see the related links.