Vault 10 is the Vault where Twig originates from.The vault itself is never actually seen in the series,only mentioned by Twig in passing
The Vault's social experiment was to record how Vault dwellers would cope with an incredible amount of food, capable of being dispensed at any given moment. Combined with the fact that the Vault had no exercise facilities, the Vault Dwellers soon began to become chronically overweight. With overweight people becoming the norm, the Vault soon developed a hierarchy based on who was the fattest. The morbidly obese were in charge and those considered merely overweight were ostracized.