In this paper, we explore time-resolved gamma-ray burst (GRB) spectra in the context of the synchrotron emission model presented by Lloyd & Petrosian in 2000. First, we show that our model—which involves three distinct emission regimes—can provide excellent fits to the time-resolved spectra of GRBs, and we present these results for a few bursts. We then describe how the phenomenological Band spectrum can be interpreted in the context of our models based on the value of the low-energy photon index α. We discuss the types of correlations one would expect to observe among the Band parameters if these models are correct. We then compare these predictions to the existing data, combining a sample of 2026 time-resolved spectra (from approximately 80 bursts). We show that the correlations found in the data are consistent with the models and discuss the constraints they place on the emission physics. In particular, we find a (~4 σ) negative correlation between the peak of the νFν spectrum Ep and the low-energy photon index α for bursts with - < α < 0, in contrast to what is predicted by the instrumental effect discussed in Lloyd & Petrosian. We suggest that this correlation is simply due to the mechanism responsible for producing values of α above the value of - —namely, a decreasing mean pitch angle of the electrons. We also show that Ep is correlated with the photon flux and interpret this as a result of changing magnetic field or characteristic electron energy between emission episodes. Finally, we discuss the implications that our results have on particle acceleration in GRBs and prospects for further testing these models with the anticipated data from the High Energy Transient Explorer 2, Swift, and the Gamma-Ray Large Area Space Telescope.