We study the spatially resolved (sub-kpc) gas velocity dispersion ($sigma$)--star formation rate (SFR) relation in the FIRE-2 (Feedback in Realistic Environments) cosmological simulations. We specifically focus on Milky Way mass disk galaxies at late times. In agreement with observations, we find a relatively flat relationship, with $sigma approx 15-30$ km/s in neutral gas across 3 dex in SFRs. We show that higher dense gas fractions (ratios of dense gas to neutral gas) and SFRs are correlated at constant $sigma$. Similarly, lower gas fractions (ratios of gas to stellar mass) are correlated with higher $sigma$ at constant SFR. The limits of the $sigma$-$Sigma_{rm SFR}$ relation correspond to the onset of strong outflows. We see evidence of on-off cycles of star formation in the simulations, corresponding to feedback injection timescales of 10-100 Myr, where SFRs oscillate about equilibrium SFR predictions. Finally, SFRs and velocity dispersions in the simulations agree well with feedback-regulated and marginally stable gas disk (Toomres $Q =1$) model predictions, and the data effectively rule out models assuming that gas turns into stars at (low) constant efficiency (i.e., ${rm 1%}$ per free-fall time). And although the simulation data do not entirely exclude gas accretion/gravitationally powered turbulence as a driver of $sigma$, it appears to be strongly subdominant to stellar feedback in the simulated galaxy disks.
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