Vitamins are those organic compounds needed by an animal to survive and be healthy, but which cannot be made, or made in sufficient quantity, by the body, so need to be obtained from the diet.
Vitamins are defined according to the role they play in maintaining health, for example, Vitamin C is needed for the manufacture of collagen.
Insufficient dietary amounts of a vitamin result in a deficiency disease: in the case of Vitamin C, this is scurvy, which has symptoms of sores on the skin and soft bleeding gums. Eventually all the mucous membranes are affected and death can result.
Different types of animals have different vitamin requirements: dogs can make Vitamin C, for example, so it is not a vitamin for them!