  We present an analysis of the global and spatially-resolved Kennicutt-Schmidt
(KS) star formation relation in the FIRE (Feedback In Realistic Environments)
suite of cosmological simulations, including halos with $z = 0$ masses ranging
from $10^{10}$ -- $10^{13}$ M$_{\odot}$. We show that the KS relation emerges
and is robustly maintained due to the effects of feedback on local scales
regulating star-forming gas, independent of the particular small-scale star
formation prescriptions employed. We demonstrate that the time-averaged KS
relation is relatively independent of redshift and spatial averaging scale, and
that the star formation rate surface density is weakly dependent on metallicity
and inversely dependent on orbital dynamical time. At constant star formation
rate surface density, the `Cold \& Dense' gas surface density (gas with $T <
300$~K and $n > 10$~cm$^{-3}$, used as a proxy for the molecular gas surface
density) of the simulated galaxies is $\sim$0.5~dex less than observed at
$\sim$kpc scales. This discrepancy may arise from underestimates of the local
column density at the particle-scale for the purposes of shielding in the
simulations. Finally, we show that on scales larger than individual giant
molecular clouds, the primary condition that determines whether star formation
occurs is whether a patch of the galactic disk is thermally Toomre-unstable
(not whether it is self-shielding): once a patch can no longer be thermally
stabilized against fragmentation, it collapses, becomes self-shielding, cools,
and forms stars, regardless of epoch or environment.
