The vibrance and saturation parameters in Lightroom or Photoshop are often confused. While both are used to intensify colors, they still operate very differently from each other. Let's take a look at the subtle but fundamental difference and when to apply which one.
Saturation controls the intensity or richness of colors in a uniform manner, not taking into account the starting point. This means as pale colors become more saturated, already prominent colors will blow out even more or eventually clip, producing strange unrealistic looking effects.
Saturation therefor in most cases is only applied very sparsely or used on a tone by tone basis, in order to maintain a realistic color correction. The Hue/Saturation adjustment layer provides a convenient way to either adjust the master saturation or certain color regions selectively, e.g. only the blues, cyans, reds, etc.
While saturation can greatly improve landscape, architecture and object photography, it can be hard to use with people photography, as skin tones in particular quickly turn orange and unpleasing.
This is where vibrance comes in. A smart algorithm distinguishes pale, muted colors from those already strong and intense so clipping is minimized. In other words: Vibrance has a higher effect on lower-saturated colors and applies less strongly to higher-saturated ones. It also prevents skin tones from becoming overly saturated and ugly. Think of vibrance as "smart saturation".
As a general rule - unless artistically desired otherwise - colors in every piece of art, photography or movie should be harmonic and pleasing. However, color harmony can be a subjective issue. A look that works for you might not work for your viewer's eye. Programs like Adobe Color CC offer guidelines and suggestions of groupings of colors that work well with each other, according to the principles of color theory. It is always a good idea to train your eye for color and develop a fundamental understanding of balance and emotions produced by certain colors.