Gluconeogenesis

Gluconeogenesis is the liver's — and to a lesser degree the kidney's — synthesis of new glucose from lactate, glycerol and glucogenic amino acids. It runs continuously at a low rate and steps up during fasting, prolonged exercise and carbohydrate restriction.

It matters because it explains why blood glucose does not collapse when you stop eating carbohydrate. Certain tissues, notably red blood cells, require glucose absolutely; gluconeogenesis guarantees a supply regardless of diet, which is why dietary carbohydrate is not, strictly speaking, essential.

In practice this is also the mechanism behind the concern about muscle loss during aggressive dieting: with protein intake too low, amino acids drawn from muscle become a convenient substrate. Adequate protein and resistance training are what protect against that.