CO2 dissolves in seawater, and then reacts with the water so that it disassociates into several ions. This disassociation means that the oceans can hold a lot of carbon – 85% of the active reservoir on Earth. Cold seawater can hold more CO2 than warm water, so waters that are cooling (i.e. poleward-moving western boundary currents) tend to take up carbon, and waters that are upwelling and warming (i.e. coastal zones and the tropics) tend to emit carbon. This is the basic reason for the pattern of the global sea-to-air CO2 flux as estimated by Takahashi et al.  in the figure at right.
The ocean is also teeming with plant life that photosynthesizes in the presence of nutrients and sunlight and makes organic matter out of the seawater CO2. Though much of the CO2 removed from seawater biologically is quickly recycled back to CO2 by the surface ocean food web, a small portion (<1%) of the waste matter sinks down into the deep and enriches the abyss with carbon. This process moves carbon from the surface ocean to the deep ocean and stores carbon away from the atmospheric reservoir. Here’s a nice video from NASA on ocean phytoplankton and their global importance.
As humans increase the atmospheric CO2 concentration, more carbon is driven into the oceans. Of all the CO2 put into the atmosphere by humans since pre-industrial times, the ocean has taken up about half (118 +- 19 PgC/yr by 1994, Sabine et al. 2004). This carbon is almost all in the surface 1km of ocean and has not penetrated any deeper because the ocean takes about 1000 years to mix completely. For the 1990’s, ocean models and a variety of data-based approaches suggest that the ocean sink was 2.2+-0.4 PgC/yr.
The Future of Ocean Carbon Uptake
Scientists expect that the ocean will eventually take up about 85% of anthropogenic CO2, but because the ocean takes ~1000 years to mix, this process will take many hundreds to thousands of years. Through 2100, an increasing sink is expected because the increasing CO2 in the atmosphere will drive more carbon into the ocean by the solubility mechanism. However, because of the chemistry of carbon in seawater, the ability of the ocean to absorb carbon decreases as the concentration increases. Anthropogenic forcings may slow down the large-scale overturning circulation of the ocean and reduce the efficiency of the ocean sink. Predictive models suggest significant regional changes in biological removal of carbon to the deep ocean, but a small net effect on globally-integrated ocean carbon uptake.
Currently, there is scientific debate about whether observations and models are already able to illustrate the declining ability of the ocean to absorb anthropogenic carbon [Canadell et al. 2007; LeQuere et al. 2009; Khatiwala et al. 2009; Knorr 2009].
Uncertainties in the ocean carbon uptake include the degree to which ocean circulation will change with climate warming and how this will modify carbon uptake. Model predictions suggest small future changes to the “biological pump” of carbon to the deep ocean, but these models do not account for potentially-important ecosystem shifts or for changes in carbon cycling in the near-surface ocean. Carbon cycling in coastal systems, including estuaries and marshes and the continental shelves is poorly quantified. These are areas of active research. The Ocean Carbon and Biogeochemistry program promotes and coordinates these research activities in the US, as does CarboOcean in Europe.
The “Other CO2 Problem” = Ocean Acidification
There are additional consequences to the ocean’s uptake of carbon. CO2 dissolved in seawater and forms carbonic acid, and so adding more CO2 to the water makes the ocean more acidic. From preindustrial times to present the pH of the ocean has declined 0.1 pH units, from 8.21 to 8.10, and it is likely to decline by another 0.3-0.4 pH units by the 2100, assuming atmospheric pCO2 is about 800 ppmv by that time. Acidification will damage coral reefs and likely place significant stress on species important to ocean food chain, particularly in the Southern Ocean. Scientists are working hard to better-understand the impacts on organisms and the integrated effects on ocean ecosystems. Here is a video from National Resources Defense Council on ocean acidification. For more detail, see these pages from NOAA and the Woods Hole Oceanographic Institution.
Canadell et al. (2007) Contributions to accelerating atmospheric CO2 growth from economic activity, carbon intensity and efficiency of natural sinks. Proc. Natl. Acad. Sci. USA 104 18866-18870. doi:10.1073/pnas.0702737104.