We present an analysis of the global and spatially-resolved Kennicutt-Schmidt 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$_{⊙}$. We show that the Kennicutt-Schmidt (KS) relation emerges robustly due to the effects of feedback on local scales, independent of the particular small-scale star formation prescriptions employed. This is true for the KS relation measured using all of the gas and using only the dense (molecular) gas. 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 ($∝ Z^{1/4}$). 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. ; Comment: 15 pages, 10 figures, submitted to MNRAS