Think it as smart saturation.
Increasing a photo's vibrance will bring up the colors in areas that have weak saturation, while areas that have high saturation levels remain unaffected. Vibrance is especially useful for bringing up the colors in photos of people. It is very kind on skin tones because it will not over saturate them, causing the colors to be unrealistically bright. Most of the time, you will find the results you're looking for by changing the vibrance instead of the saturation because it does not affect every pixel in the image.