Gravitational sinking of organisms (or the remains of organisms) transfers particulate organic carbon from the surface waters of the ocean to its deep interior.  This process is known as the biological pump, and quantifying it is of interest to scientists because it is an important aspect of the Earths carbon cycle.  Essentially, this is because carbon transported to the deep ocean is isolated from the atmosphere, allowing the ocean to act as a reservoir of carbon.  This biological mechanism is accompanied by a physico-chemical mechanism known as the solubility pump which also acts to transfer carbon to the oceans deep interior.
Measuring the flux of sinking material (so-called marine snow) is usually done by deploying sediment traps which intercept and store material as it sinks down the water column.  However, this is a relatively difficult process, since traps can be awkward to deploy or recover, and they must be left in situ over a long period to integrate the sinking flux.  Furthermore, they are known to experience biases and to integrate horizontal as well as vertical fluxes because of water currents.  For this reason, scientists are interested in ocean properties that can be more easily measured, and that act as a proxy for the sinking flux.  The f-ratio is one such proxy.