There are two main forms of Carbon in the ocean. The Carbonates that make up the bulk of corals and sea shells and dissolved Carbon Dioxide.
Organisms in the ocean take Carbon Dioxide and turn it into carbonate ##CO_3^(2-)##. Carbonate is often combined with ions like ##Ca^(2+)## and ##Mg^(2+)##.
The Calcium Carbonate makes up the hard structures of corals, and sea shells. The amount of Carbon in the Coral reefs far exceeds the amount of Carbon Dioxide dissolved in the oceans.
The Carbon Dioxide in dissolves into the oceans. This acts as a buffer to the increases in the level of Carbon Dioxide in the atmosphere.
If the level of Carbon Dioxide in the atmosphere more of the gas dissolves into the ocean. If the levels of Carbon Dioxide decrease more Carbon Dioxide would come out of solution and redissolve into the atmosphere.