The ocean is called the carbon sink because there is mass amounts of carbon all the way at the bottom. How did the carbon get there?

There is absorption of carbon dioxide by the oceans through physicochemical (air-sea surface exchange) and biological processes. During physicochemical process, molecules of CO2 get into the ocean by diffusing into the sea surface waters and dissolving. Various factors such as wind, sea surface mixing, concentrations of CO2, and the temperature of the water influences the amount of CO2 that diffuses and dissolves in the ocean surface water. Also, during biological processes, dead cells, shells and other parts of dead organisms get decayed and releases carbon dioxide at the bottom of the water.