  (ABBREVIATED) The extraordinary 1998 August 27 giant flare places strong
constraints on the physical properties of its source, SGR 1900+14. We make
detailed comparisons of the published data with the magnetar model. The giant
flare evolved through three stages, whose radiative mechanisms we address in
turn. A triggering mechanism is proposed, whereby a helical distortion of the
core magnetic field induces large-scale fracturing in the crust and a twisting
deformation of the crust and exterior magnetic field. The envelope of the
pulsating tail of the August 27 flare can be accurately fit, after ~40 s, by
the contracting surface of a relativistically hot, but inhomogeneous, trapped
fireball. We quantify the effects of direct neutrino-pair emission, thereby
deducing a lower bound ~ 10^{32} G-cm^3 to the magnetic moment of the confining
field. The radiative flux during the intermediate ~40 s of the burst appears to
exceed the trapped fireball fit. The spectrum and lightcurve of this smooth
tail are consistent with heating in an extended pair corona, possibly powered
by continuing seismic activity in the star. We consider in detail the critical
luminosity, below which a stable balance can be maintained between heating and
radiative cooling in a confined, magnetized pair plasma; but above which the
confined plasma runs away to local thermodynamic equilibrium. In the later
pulsating tail, the best fit temperature equilibrates at a value which agrees
well with the regulating effect of photon splitting. The remarkable four-peaked
substructure within each 5.16-s pulse provides strong evidence for the presence
of higher magnetic multipoles in SGR 1900+14. The corresponding collimation of
the X-ray flux is related to radiative transport in a super-QED magnetic field.
