“Bouncing” light is simply the use of a reflector on the shadow side of your subject. While I own multiple professional reflectors, I honestly use plain old white foam core more than anything else. It’s cheap, lightweight and doesn’t cast a color on my subject like gold and silver reflectors do. I dig it.
So when should you use a reflector? When you want to lighten your shadows or create a more evenly lit subject. For example, if you have a single light source and it’s coming from the side, half of your subject will be bright and half will be dark. If you are going for a more dramatic and moody shot, then you may choose to leave the dark side as is, perhaps even deepening the shadows by using a black board where you would hold a reflector. But if you want a light, airy feeling to your image, you would want to use a reflector. By holding a white board up on the shadow side of your subject, your light will hit the board and “bounce” back on to the dark areas, in effect lightening them.
Several years ago I shot a breakfast cookbook and, because the photos in the book were meant to feel like they were taken in the morning, I used reflectors constantly. It just made sense. However, when I shoot work for myself, I tend to prefer a more dramatic look (I love me some shadows) and so I usually avoid using a reflector. It's all about your personal preference. :)