The phrase "sediment surface" refers to the top layer of small particles that settle at the bottom of bodies of water or on the ground. Full definition
Below the sediment surface there is plenty of hydrogen sulfide and carbon for bacteria to consume via oxidation, or removing electrons, but the electron acceptor is up at the sediment surface, in the form of dissolved oxygen in the overlying water. (scientificamerican.com)
When the researchers switched the electric current off by deoxygenating the water, thereby removing the electron acceptor at the sediment surface, the depth of the hydrogen sulfide layer in the sediment rose in less than an hour, as deeper microbes could no longer consume it. (scientificamerican.com)
So the bacteria evidently form a sort of conductive chain, comprising biological nanowires and possibly pyrite grains embedded in the mud, that allows electrons from the oxidation of hydrogen sulfide and carbon within the sediment to contribute to the reduction of oxygen by other microbes at the sediment surface. (scientificamerican.com)