The best Wildlife photography will always show a crystal-clear animal against a blurry background. This is done by using just the right combination of lens, aperture, and shutter speed, and really helps to make the subject stand out. If a background of branches and leaves were as sharply focused as the bird in the foreground, it would be very easy to lose the bird in the background “noise.”
You can use photo editing techniques to achieve the same effect.
Load your picture into your favorite photo editing program. Using a selection tool like a “Lasso,” select the foreground image, the “animal” that has to be set off from the “leaves and branches.” Once it’s selected, “Invert” the selection. Most photo editing programs have this option. In effect, it means “swap the selected areas for the unselected ones.” By inverting, you’ll select only the background of your image. If your program has the feature, you might also consider Feathering your selection. This helps to break up the outline of the selection, so that it doesn’t have such a sharp edge to it.
Once the background is highlighted, use a tool called Gaussian Blur. This is a specific type of blurring routine designed to imitate the blurring that happens in traditional photography. Don’t be afraid to experiment with the settings, but remember that a little bit of blur–leaving the background out of focus, but recognizable–is better than a lot.
A related photo technique is called Panning. Focus on a moving object, like a racecar, and keep the camera pointed at that object as it goes by. Done properly, the racecar will be in focus, while the crowd behind it will be blurred. This kind of blur is called Motion blur, or sometimes Radial blur. Using Radial instead of Gaussian will make your subject appear to be racing past the background.