How does shivering help when its cold?

Answer 1

When you exercise, the a by product of the conversion of glucose & sugar to movement in the cells is heat. The mitochondria in the cells produce this when breaking down ATP. Shivering is merely an exercise, even if autonomic, so done with no conscious effort, so as the muscles rapidly contract, they require & burn energy.

Rubbing your hands together on the other hand creates friction, which converts the movement energy to heat, much like a cars braking system.

Answer 2

Shivering is made by muscle work, that itself produces heat, as not all muscle energy expenditure transforms in kinetic force, because the ATP conversion is not perfect - no machine or mechanism are, including the biological ones!

Besides this fact, there are other components that account for the accumulation of heat by the body; the blood of the animal is deviated from skin and superficial mucosa to deeper - cold hands, lips and feet - to diminishes the loss of hot; in general, the behavior of the animal changes to a "warm itself"; tend to look for hotter places, cover itself. For animals with a lot of thicker pile - like chimpanzee - the piloerection component serve as an entrapment of hot air, functioning as a blanket.

Hypothalamus is the central organizer of this response.