We present a spectroscopic study of the unusual flaring activity of the cataclysmic variable AE Aqr, which makes use of time-resolved, ultraviolet spectra obtained with the Hubble Space Telescope in November of 1992. This study complements our earlier investigation of the coherent, 33 s oscillations of AE Aqr using the same data. Its scientific objective is to define the ultraviolet spectroscopic properties of the flares and to use them to constrain scenarios for their origin. We find that the UV spectrum of flares features a plethora of emission lines and a prominent Balmer recombination continuum. During flares, the emission-line and continuum fluxes increase by a factor of several, they vary together, with no easily discernible time lag, and proportionally to each other. The radial velocity curves of the stronger ultraviolet lines lead the radial velocity curve of the companion star by about one-third of a cycle, much like the radial velocity curves of the Balmer lines. Our observational results, taken together with other known properties of the system, support a recently proposed scenario in which the accretion flow from the companion star is fragmented into discrete blobs that interact with the speedy propeller that is the magnetosphere of the rapidly spinning white dwarf. Scenarios attributing the flares to coronal activity on the companion star or a magneto spheric gating instability at the white dwarf are ruled out by the data. Their main shortcoming is that they cannot account for the kinematic signature of the line-emitting gas.In the context of the fragmented accretion flow/magnetic propeller scenario we propose that the flares represent the excitation of gaseous blobs upon encounter with the propeller, and their subsequent radiative cooling as as they are expelled from the system. From the data we estimate the mass of a typical blob from which we derive a mean mass transfer rate from the companion star. This mass transfer rate is considerably larger (4 orders of magnitude) than the rate of accretion onto the white dwarf inferred from the X-ray luminosity, as one would expect in the propeller scenario. Moreover, the power expended by the propeller in ejecting most of the matter in the blobs from the system can account for the observed spin-down of the white dwarf. Additional attractive features of this scenario include its ability to explain the observed quasi-periodic oscillations, and the observed pulsed γ-ray emission from AE Aqr.