The keto, or ketogenic diet, is characterized by a marked reduction in the consumption of carbohydrates (the family of sugars) and proteins and by an increase in the proportion of energy that comes from fat. Although it's very fashionable these days, it was invented in the 1920s to reduce seizures in children with epilepsy and reduce the amount of medication they take. It is still used today at the CHU Sainte-Justine to treat children with epilepsy.
The diet “works” when you manage to reach the state of ketosis. The claimed benefits of ketosis are numerous:
Lose weight quickly;
Slow down the appearance of the feeling of hunger;
Stabilize the energy level during the day;
Reduce the symptoms of epilepsy;
etc
Unsurprisingly, it therefore meets all the criteria of a diet born to be popular:
Promising rapid weight loss;
Eliminate one or more food groups;
Be restrictive;
Forcing you to eat differently from your friends or family;
Have scientific bases which give it a little sexy side;
Be supported by public figures.