We present spectroscopy and 1'' narrow-band imaging of near-infrared line emission in the central 0.3 pc of the Galaxy. The ''mini-cavity'' region 3.''5 southwest of the compact radio source Sgr A* is a source of bright 2.2178 mum line emission that is now unambiguously identified as [Fe III] by detection of three additional [Fe III] lines. The derived fractional abundances of [Fe]/[H] greater-than-or-equal-to 2.5 x 10(-5) and [Fe++]/[Fe+] almost-equal-to 1 together with the observed spatial distributions and line profiles of [Fe III] and H I Brgamma suggest the following model of the mini-cavity region. A fast (greater-than-or-equal-to 1000 km s-1) wind from one or several sources within a few arcsecs of the present location of the mini-cavity blows into the partially neutral gas streamer(s) orbiting the dynamic center of the Galaxy and creates an expanding gas bubble. Fast shocks triggered by this interaction heat and compress the streamer gas, destroy dust grains, and release iron into the gas phase. After cooling, the dense post-shock gas is maintained at about 7000 K electron temperature through photoionization by the central UV field. Charge exchange with neutral hydrogen in the streamer gas maintains a reasonably large fraction of singly ionized iron. The dense, hot shocked wind is expected to be a strong source of soft X-rays. The estimated X-ray luminosity is consistent with Einstein observations of the Galactic center. Morphology and bubble dynamics can be explained either by models invoking He I emission-line stars as a local wind source or, perhaps more likely, by models in which a jet from Sgr A* acts as an external wind source.