What was done
The thirteen scientists from Australia, France, Germany, Russia, the United Kingdom and the United States who conducted this massive study employed six coupled climate model simulations to determine - to a very rough first approximation - the biological response of the global ocean to the climate warming they simulated for the period between the beginning of the Industrial Revolution and the year 2050.  Based on vertical velocity, maximum winter mixed-layer depth and sea-ice cover, they defined six biomes and calculated how their surface geographies changed in response to their calculated changes in global climate.  Next, they used satellite ocean color and climatological observations to develop an empirical model for predicting surface chlorophyll concentrations from the final physical properties of the world's oceans as derived from their global warming simulations, after which they used three primary production algorithms to estimate the response of oceanic primary production to climate warming based on their calculated chlorophyll concentrations.

What was learned
When all was said and done, Sarmiento et al. arrived at a global warming-induced increase in global ocean primary production that ranged from 0.7 to 8.1%.

What it means
The final answer seems a far, far cry from the disastrous consequences routinely predicted by climate alarmists.  In fact, it's actually a tad positive.  As mentioned above, however, this result is still very crude and will undoubtedly be revised again and again as important advances are made in all of the many sub-routines that come together to produce the final result.