Dodge and burn is one of the most useful tools a photographer should have in his arsenal. Although it doesn't necessarily mean using the Dodge and Burn tool in the Photoshop Palette. Dodging and Burning can be achieved in a number of ways. It can be done by adding a Levels layer and masking parts of it over the image to isolate the effects. It can be painting white or black on a transparent layer and blending it on the image. However you want to do it, Dodging and Burning is just darkening or lightening up parts of an image.

Why use it? Dodge and burn has lots of uses. It can be to balance highlights, retain details, correct lighting, add depth or simply, make an image more dramatic. You will need to play around with this tool to really get a grip on its use. Using it regularly will help you find out when and where to use it.

Here are some samples of it's usage.

On Portraiture, it can be used to correct or improve lighting (instead of reshooting)

(Move your mouse over the images to view original pictures)

Here I made the background darker but left some light across the face to direct the viewer's eyes onto the face of the model. This would have been difficult to do during the shoot with available light and limited equipment.

Here, again, I burned the background to make the subjects pop out and add texture to it. Giving the image more depth.

Here, again, background darker, and, burned and saturated some parts of the face to add depth.

On Landscapes, it can be used to remove unwanted highlights, make the sky bluer and darker, add details (especially to the clouds), and more.

Here, made the sky darker and added detail to the clouds using the burn tool.

Here, did some levels, saturation and a whole lot more. Dimmed the lights on the right part of the image to keep the attention on the subject.

I have more samples but I guess you get the idea.

Try to play around with the dodge and burn tool. Use it everytime you edit your photos, just so you'll have an idea how it affects your images. Once you master it, you'll wonder how you got along all this time without it. The bad side about it is, more wasted post-processing time.