  We present a simple, redshift-independent analytic model that explains the
local Fundamental Metallicity Relation (FMR), taking into account the physical
processes of star formation, inflow of metal-poor intergalactic medium (IGM)
gas, and the outflow of metal rich interstellar medium (ISM) gas. We show that
the physics of the FMR can be summarised as follows: for massive galaxies with
stellar mass M_* >= 10^11 solar masses, ISM metal enrichment due to star
formation is compensated by inflow of metal poor IGM gas, leading to a constant
value of the gas metallicity with star formation rate (SFR); outflows are
rendered negligible as a result of the large potential wells of these galaxies.
On the other hand, as a result of their smaller SFR, less massive galaxies
produce less heavy elements that are also more efficiently ejected due to their
shallow potential wells; as a result, for a given M_*, the gas metallicity
decreases with SFR. For such galaxies, the outflow efficiency determines both
the slope, and the knee of the metallicity-SFR relation. Without changing any
parameters, this simple model is also successfully matched to the gas fraction
- gas metallicity relation observed for a sample of about 260 nearby galaxies.
