Carbon and its compounds are used in a large number of operations in and around us. The most common form of carbon that we have all seen and used is the lead of the pencil, which is nothing but graphite (a form of carbon). Another form of carbon, commonly in use, is diamond, which is used in jewelry. Carbon is the key to class of compounds known as hydrocarbons, which include everything from fuels to food and macromolecules in our body. The food that we eat is full of hydrocarbons (i.e. carbon compounds) and food is the only source of energy and nutrients that we have. All the fossil fuels around us (say, gasoline, diesel, natural gas, kerosene, etc.) are also hydrocarbons. Carbon is also present in steel, which has many applications in our life (think about the body of automobiles, or the structure of tall buildings). In general, carbon and its compounds are present practically everywhere.
Hope this helps.