Add more natural light to the scene
A reflector is exactly what it name implies: an object that reflects light. The more important information is when and why you might want to use one.
When A Reflector Helps
Say that you are taking a photograph of your best friend outside. The sunlight is landing on the left side of their face, casting the right side into shadow.
A reminder about digital cameras: they do not handle severe contrast very well. So what happens in the scene described above? If you expose for the sunlit side of your friend's face, the side that is in shadow will be completely dark and without detail.
If you don't want the dark side of their face to completely disappear, you need to reflect some light on it. Place the reflector to their right side (the shadow side) and the additional light will reduce the contrast. Now you can capture detail in both sides of their face.
This concept of reflected light will work even if you aren't taking a portrait. Say that you have a flower in the shade and want to give it a touch of light. Break out the reflector. Maybe you have a pet indoors and there isn't enough light to use a fast shutter speed — a reflector can help.
Types of Reflectors
There are several different types of reflectors, depending upon just how much light you want to reflect. A white reflector will add a moderate amount of light. A silver reflector will add a lot of light to the scene. A gold reflector will not only reflect light, it will also warm it up, which is nice for portraits.
I mention this last one separately, since it goes against the concept of reflected light: you can get a black reflector. If the other reflectors add light, this one reduces it. But what's the point?
A black reflector is most useful when you want to eliminate reflections from glass and plastic. Say that you are taking a photo through a window. The window reflects the ambient light. With a properly positioned black reflector, you can eliminate the reflection and get a clear shot.
Photo One — No Reflector
No reflector is used in this first photograph. There is a lot of contrast in the photo (a wide range from light to dark). The areas in shadow appear almost black, and there is no detail apparent.
Sometimes this may be the look that you want in your photograph. If that is the case, leave the light as is.
However, if you are looking for an image with less contrast and more shadow detail, you need to reflect some light into those areas to make the light on your subject more even.
Photo One — Reflector
Same photograph, same angle, only this time a reflector has been used. Notice how there is suddenly more detail in the shadow side of the face.
Some shadow remains so that the face has contour and dimension, but its intensity has been reduced.
Reflectors can help out a lot with natural light portrait photography when you need more detail in the shadows. While they are bulky and do take some getting used to, eventually you will learn how to position them for maximum effect.