  Despite decades of investigations, the physical mechanism that powers the
bright prompt $\gamma$-ray emission from gamma-ray bursts (GRBs) is still not
identified. One important observational clue that remains not properly
interpreted so far is the existence of time lags of broad light curve pulses in
different energy bands, named "spectral lags". Here we show that the
traditional view invoking the high-latitude emission "curvature effect" of a
relativistic jet cannot account for spectral lags. Rather, the observed
spectral lags demand the sweep of a spectral peak across the observing energy
band in a specific manner. The duration of the broad pulses and inferred
typical Lorentz factor of GRBs require that the emission region is in an
optically thin emission region far from the GRB central engine. We construct a
simple physical model invoking synchrotron radiation from a rapidly expanding
outflow. We show that the observed spectral lags appear naturally in our model
light-curves given that (1) the gamma-ray photon spectrum is curved (as
observed), (2) the magnetic field strength in the emitting region decreases
with radius as the region expands in space, and (3) the emission region itself
undergoes rapid bulk acceleration as the prompt $\gamma$-rays are produced.
These requirements are consistent with a Poynting-flux-dominated jet abruptly
dissipating magnetic energy at a large distance from the engine.
