Butter is essentially the milk fat, most frequently made from cows’ milk. Butter is produced from milk cream, processed to separate fat from the liquid part, or Buttermilk. Its color may vary from whitish to a deep yellow. On the market, you usually find butter containing 80% butterfat and 15% water, even if traditionally made butter may have a higer water content.
If you heat butter to its melting point and then allow it to cool down, and then remove the skin of whey proteins formed at the top, you get clarified butter, a sort of almost-pure butterfat, with a higher smoke point and a much longer shelf life than regular, fresh butter.
In cooking, Butter can be used as a spread or to make sauces, but above all to make baking desserts or other baking products. Its high fat content makes it perfect to withstand high temperatures. And, besides, its flavor is perfect for pastry making. Anyway, it is also used for sautéing and frying.
Fun fact: Butter is a good source of vitamin A. Despite being a milk product, its lactose content is very low, so it can be tolarated by lactose intolerants (but not by people with milk allergy, as it still contains casein, the milk protein responsible for most milk allergies). Anyway, you should make a sparing use of it, as it will increase the calorie content of any recipe.