The term curry includes many dishes that are part of the Indian cuisine. They include many spices or herbs. Many of these spices could be hot because they include chilies. Curry is spicy because it includes some spices that create heat in the mouth like ginger, pepper, chilies and mustards. The number one ingredient in hot spices is called capsaicin.
This is what causes the spices hot on your tongue. Your tongue has many receptors on it that experience pain which is heat from the capsaicin. In order to stop the heat from continuing, you will want to stop eating. However, it will continue to burn until you do something about it. Some people drink cold water or start eating something bland.
The biggest reason Indian curries are so spicy is because spice kills bacteria and microbes that so rapidly grows in the country's hot climate. This means prevention of food-borne illness and the added benefit of micronutrients found in trace amounts. The heat index is cause for another reason as to why India's food is so spicy—peppery foods make people sweat, and sweating helps cool them.
Consumption of spicy food also seems to be genetic—if your parents and grandparents ate peppered and spicy foods, it is likely you will enjoy the same. Plenty of spices used in Indian food aren't what most people consider to be truly spicy, but the longer you cook a spice, the stronger it becomes; most Indian dishes are cooked on low over a long period of time.
