  The unusually short durations, high luminosities, and high photon energies of
the Crab Nebula gamma-ray flares require relativistic bulk motion of the
emitting plasma. We explain the Crab flares as the result of randomly oriented
relativistic "minijets" originating from reconnection events in a magnetically
dominated plasma. We develop a statistical model of the emission from Doppler
boosted reconnection minijets and find analytical expressions for the moments
of the resulting nebula light curve (e.g. time average, variance, skewness).
The light curve has a flat power spectrum that transitions at short timescales
to a decreasing power-law of index 2. The flux distribution from minijets
follows a decreasing power-law of index ~ 1, implying the average flux from
flares is dominated by bright rare events. The predictions for the flares'
statistics can be tested against forthcoming observations. We find the observed
flare spectral energy distributions (SEDs) have several notable features: A
hard power-law index of p ~< 1 for accelerated particles that is expected in
various reconnection models, including some evidence of a pile-up near the
radiation reaction limit. Also, the photon energy at which the SED peaks is
higher than that implied by the synchrotron radiation reaction limit,
indicating the flare emission regions' Doppler factors are ~> few. We conclude
that magnetic reconnection can be an important, if not dominant, mechanism of
particle acceleration within the nebula.
