The physical conditions near the optical continuum peak ("hot spot") in the inner narrow-line region of the Seyfert 2 galaxy NGC 1068 are examined using ultraviolet and optical spectra and photoionization models. The spectra were taken with the Hubble Space Telescope/Space Telescope Imaging Spectrograph (STIS) through the 0 ".1 x 52 ".0 slit, covering the full STIS 1200-10000 Angstrom waveband, and are from a region that includes the hot spot, extending 0 ".2, or similar to 14 pc (for H-0 = 75 km s(-1) Mpc(-1)), in the cross-dispersion direction. The spectra show emission lines from a wide range of ionization states for the most abundant elements, similar to archival Faint Object Spectrograph spectra of the same region. Perhaps the most striking feature of these spectra is the presence of strong coronal emission lines, including [S XII] lambda 7611, which has hitherto been identified only in spectra of the solar corona. There is an apparent correlation between ionization energy and velocity of the emission lines with respect to the systemic velocity of the host galaxy, with the coronal fines blueshifted, most other high-excitation lines near systemic, nd some of the low-ionization lines redshifted. From the results of our modeling, we find that the emission-line gas is photoionized and consists of three principal components: (1) one in which most of the strong emission lines, such as [O III] lambda 5007, [Ne V] lambda 3426, and C IV lambda 1550, arise; (2) a more tenuous, highly ionized component, which is the source of the coronal-line emission; and (3) a component, which is not coplanar with the other two, in which the low-ionization and neutral lines, such as [N II] lambda 6548 and [O I] lambda 6300, are formed. The first two components are directly ionized by the EUV-X-ray continuum emitted by the central source, while the low-ionization gas is ionized by a combination of highly absorbed continuum radiation and a small fraction of unabsorbed continuum scattered by free electrons associated with the hot spot. The combination of covering factor and Thomson optical depth of the high-ionization components is insufficient to scatter the observed fraction of continuum radiation into our fine of sight. Therefore, the scattering must occur in an additional component of hot plasma, which contributes little or no UV/optical line emission.