We present Hubble Space Telescope (HST) narrow-passband H alpha and [S II] images and broadband continuum images of the region around an extremely luminous optical and X-ray supernova remnant complex in the spiral galaxy NGC 6946. These images, obtained with the PC1 CCD of the Wide Field Planetary Camera 2, show a circular, limb-brightened shell of diameter 0.35 " [9 d/(5.1 Mpc) pc] superposed on the edge of a larger, lower surface brightness elliptical shell (1.4 " x 0.8 ", or similar or equal to 34 pc x 20 pc). The HST images allow us to see that the [S II]:H alpha ratio remains high across both shells, indicating that both are collisionally heated. A brightening of the H alpha and [S II] line emission arises on the eastern side of the smaller shell, where it is apparently interacting with the western edge of the larger shell. Our HST V image includes the nebula's strong [O III] lambda 5007 emission in the blue wing of the filter, providing a glimpse at the [O III] nebular morphology. The smaller shell looks similar, but the extended structure looks sharper than in H alpha and [S II] images, reminiscent of a cavity wall. The HST and ground-based continuum images show the brightest members of the underlying and adjacent stellar population, indicating the presence of massive OB stars in and near the region. A new optical ground-based spectrum confirms that the [N II]:H alpha ratio is enhanced in the region, consistent with mass loss from massive stars. These data show an average ([S II] lambda lambda 6716, 6731): Ha ratio across both shells of similar to1 and a mean electron density of similar to 400 cm(-3), indicating preshock densities of order 10 cm(-3). We interpret this nebular morphology and supporting information as an indication of multiple supernova explosions in relatively close temporal and spatial proximity. We discuss possible scenarios for this complex region and the reasons for its extreme luminosity.