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 larger than 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 stellar mass, the gas metallicity decreases with SFR. For such galaxies, the outflow efficiency determines both the slope, and the knee of the metallicity-SFR relation. The model is then successfully matched to results from numerical simulations including metal enrichment and feedback at higher redshifts.