By storing carbon they are meaning that the wetlands literately store CO2, and if they are allowed to break down that carbon will largely be released back into the active cycle and be part of our current atmospheric problems. Much like the oceans hold an amount CO2, a large amount because of their size, but as they heat up this is less efficient so they hold less and the excess seeps into the atmosphere.

Those areas are probably not capturing/trapping further carbon, they have probably been at an equilibrium point for quite some time with some entering & leaving the system without the overall amount not increasing, but they are effectively storing a notable amount that would be released if the properties that enable them to hold onto it degrade.