What is the purpose of the umber underpainting?
Your question is a very good one, and without an understanding as to the why, most people would not do the step. I'll give the "why" as I understand them.
All oil paints fade with time. It is however, the longest lasting paint medium we have. Acrylics are proving to be good, but we don't know what the future holds completely for this type of paint. It is a plastic, and our landfills are full of it, because nature has few things to break it down.
Because of the fading (with oils), we use an umber underlayer. It is the one color of paint that has proven to outlast others as far as fading in the future is concerned. So with it, you are establishing a base coat with all its nuances, shading, and some of your details.
The dead layer, or gray layers merely compliments this layer. primarily in the half shadows. Taking an egg for example. on the one side, you will have a bright area, on the other, you will have the dark area and shadow. But it is the in-between that is difficult to capture with just the burnt umber. The gray can be graduated so that the half shadow, transition from light to dark, is very, very smooth. The second reason is by using just a gray layer, or gray paints, you can concentrate on the modeling, shape, and some of the details and texture. Your mind is not troubled with questions like, is the green dark enough, or the blue light enough. You are strickly dealing with black and white.
In the color layer, you begin to bring your picture to life. In your dark areas, sometimes it is fine to leave the burnt umber showing through. In the half shadows, it is ok to leave some of the gray showing through. It is the well lite areas that your colors will be their brightest and truest. With each layer, you don't have to paint the entire picture again, only sections.