Bio-available nitrogen occurs in the ocean in several forms, including simple ionic forms such as nitrate (NO), nitrite (NO) and ammonium (NH), and more complex organic forms such as urea ((NH)CO).  These forms are used by autotrophic phytoplankton to synthesise organic molecules such as amino acids (the building blocks of proteins).  Grazing of phytoplankton by zooplankton and larger organisms transfers this organic nitrogen up the food chain and throughout the marine food-web.
When nitrogenous organic molecules are ultimately metabolised by organisms, they are returned to the water column as ammonium (or more complex molecules that are then metabolised to ammonium).  This is known as regeneration, since the ammonium can be used by phytoplankton, and again enter the food-web.  Primary production fuelled by ammonium in this way is thus referred to as regenerated production.
However, ammonium can also be oxidised to nitrate (via nitrite), by the process of nitrification.  This is performed by different bacteria in two stages :
:::NH + O → NO + 3H + 2e
:::NO + HO → NO + 2H + 2e
Crucially, this process is believed to only occur in the absence of light (or as some other function of depth).  In the ocean, this leads to a vertical separation of nitrification from primary production, and confines it to the aphotic zone.  This leads to the situation whereby any nitrate in the water column must be from the aphotic zone, and must have originated from organic material transported there by sinking.  Primary production fuelled by nitrate is, therefore, making use of a "fresh" nutrient source rather than a regenerated one.  Production by nitrate is thus referred to as new production.
The figure at the head of this section illustrates this.  Nitrate and ammonium are taken up by primary producers, processed through the food-web, and then regenerated as ammonium.  Some of this return flux is released into the surface ocean (where it is available again for uptake), while some is returned at depth.  The ammonium returned at depth is nitrified to nitrate, and ultimately mixed or upwelled into the surface ocean to repeat the cycle.
Consequently, the significance of new production lies in its connection to sinking material.  At equilibrium, the export flux of organic material sinking into the aphotic zone is balanced by the upward flux of nitrate.  By measuring how much nitrate is consumed by primary production, relative to that of regenerated ammonium, one should be able to estimate the export flux indirectly.
As an aside, the f-ratio can also reveal important aspects of local ecosystem function.  High f-ratio values are typically associated with productive ecosystems dominated by large, eukaryotic phytoplankton (such as diatoms) that are grazed by large zooplankton (and, in turn, by larger organisms such as fish).  By contrast, low f-ratio values are generally associated with low biomass, oligotrophic food webs consisting of small, prokaryotic phytoplankton (such as Prochlorococcus) which are kept in check by microzooplankton.