We investigate in this paper the core-collapse supernova explosion mechanism in both one and two dimensions. We verify the usefulness of neutrino-driven overturn (``convection'') between the shock and the neutrinosphere in igniting the supernova explosion. The 2-D simulation of the core of a 15$\mdot$ star that we present here indicates that the breaking of spherical symmetry may be central to the explosion itself and that a multitude of bent and broken fingers is a common feature of the ejecta. In 2-D, the steady-state shock radius is larger than its value in 1-D by 30\%--100\%. The critical condition for explosion is thereby relaxed. Since supernovae are driven by neutrino heating, they are coronal phenomena, akin to winds, though initially bounded by an accretion tamp. Neutrino energy is pumped into the supernova during the shock's propagation through the inner many thousands of kilometers and not instantaneously. Curiously, just after the explosion is triggered, the matter that will eventually be ejected is still bound. The high-speed fingers that emerge from the core seem a natural explanation for the nickel bullets seen in 87A and the shrapnel inferred in some supernova remnants. Within 100 ms of the explosion, a strong, neutrino-driven wind is blowing outward from the protoneutron star.

68 pages, AASTeX Latex, 37 Figures, Accepted for Sept. 10'th, 1995 Ap. J., Figures and mpeg simulations available at http://lepton.physics.arizona.edu:8000/