By convention, a vitamin is an essential nutrient which is NOT: a dietary mineral, essential fatty acid or essential amino acid (as these are needed in much larger amounts), or one of the many other nutrients that are useful for maintaining good health but are not required as often. Therefore, vitamins ARE: required often; can't be produced by the body; only needed in trace amounts; vital for the body to function properly.
There are currently 13 vitamin groups widely recognised for Humans. These are: Vitamin A, Vitamin B range (B1, B2, B3, B5, B6, B7, B9, B12), Vitamin C, Vitamin D, Vitamin E & Vitamin K. Each of these Vitamin Groups contains several compounds, known as Vitamer, which are not necessarily similar in structure but exhibit similar biological activity. For example Vitamin A includes: retinal, retinol and four known carotenoids including beta carotene.
All of these vitamers are in forms that are available for use by the body, though not all as easily, meaning that different dosages are required for different sources of vitamins to gain the same effect on the body. With Vitamin A for example, retinal and retinol from animal sources are much more potent and readily available to the body than the carotenoid forms of Vitamin A available from carrots.
Compounds considered as Vitamins are not the same for each animal! For example, dogs can produce their own Vitamin C so this would not be considered a Vitamin for them as it doesn't meet the criteria for vitamins (as it CAN be produced in the dogs body). In addition, some forms of each vitamin cannot be absorbed by all animals, such as the carotenoid forms of vitamin A cannot be absorbed by cats or ferrets, so are not classed as vitamins for these species.
All the vitamins are organic compounds, which mean they contain Carbon (usually carbon chains with Hydrogen and other elements attached at various places along the chain). The B range of Vitamins, and Vitamin C, are all water soluble so are excreted from the body in urine and therefore need to be replenished daily, The remainder of the Vitamins are fat soluble so do not need to be replenished so often as they are stored in the liver.
Vitamins have many different effects on the body. Some, such as Vitamin C & Vitamin E are antioxidants, whereas Vitamin A and Vitamin D regulate various bodily functions such as mineral metabolism and cell growth. The Vitamin B Complex (range) help enzymes to work properly in their roles as catalysts in metabolic reactions.
Until the mid-1930s, vitamins were only available through the food we ate (though of course Vitamin D is produced in the skin when we get enough direct sunlight). However these days vitamin supplements are widely available, both as individual vitamins and also blends containing a wide range of multivitamins & minerals.