The HESS (High Energy Stereoscopic System) collaboration recently reported highly significant detection of TeV gamma-rays coincident with Sgr A*. In the context of other Galactic center (GC) observations, this points to the following scenario: In the extreme advection-dominated accretion flow (ADAF) regime of the GC black hole (BH), synchrotron radio/submillimeter emission of similar to100 MeV electrons emanates from an inefficiently radiating turbulent magnetized corona within 20R(S) (Schwarzschild radii) of the GCBH. These electrons are accelerated through second-order Fermi processes by MHD turbulence, as suggested by Liu et al. Closer to the innermost stable orbit of the ADAF, instabilities and shocks within the flow inject power-law electrons through first-order Fermi acceleration to make synchrotron X-ray flares observed with Chandra, XMM, and INTEGRAL. A subrelativistic MHD wind subtending an similar to1 sr cone with power greater than or similar to10(37) ergs s(-1) is driven by the ADAF from the vicinity of the GCBH. As in pulsar-powered plerions, electrons are accelerated at the wind termination shock at greater than or similar to10(16.5) cm from the GCBH, and Compton-scatter the ADAF and the far-infrared dust radiation to TeV energies. The synchrotron radiation of these electrons forms the quiescent X-ray source resolved by Chandra. The radio counterpart of this TeV/X-ray plerion, formed when the injected electrons cool on timescales of greater than or similar to10(4) yr, could explain the origin of nonthermal radio emission in the parsec-scale bar of the radio nebula Sgr A West.