@AlanBoyd is right that the term 'essential sugar' is not a scientific or biologically defined term and is not true given the meaning of the word essential that is in use in biology.
In alternative health and diet circles, the term 'essential sugars' refers to a set of simple carbohydrates which are hypothesized to be important for good health and nutrition in people.
Even if this were a valid approach in humans its very unlikely to be the same specific sugars and proportions for other animals and living things.
So given all these caveats the reference I found for 'essential sugars' lists these 8: glucose, galactose, fucose, mannose, glucosamine, galactosamine, neuraminic acid, and xylose.
As far as whether this really helps us, I personally don't think this is the key to good health in and of itself. It really oversimplifies all of the biomachinery we have to break down and utilize carbohydrates.
As the diet recommends the eating of vegetables which aren't too green, avoiding fructose, it doesn't seem to hurt. Carbohydrates from food are often the product of breaking down complex carbohydrates. I feel as if watching the glycemic index of your food and avoiding soft drinks and too much fruit juice will get you further in terms of health. Avoiding simple carbohydrates entirely in your diet also has advocates and there is some medical research that backs it up.