We have examined the physical conditions in intrinsic UV-absorbing gas in the Seyfert galaxy NGC 4151, using echelle spectra obtained with the Space Telescope Imaging Spectrograph (STIS). We confirm the presence of the kinematic components detected in earlier GHRS observations as well as a new broad absorption feature at a radial velocity of -1680 km/s. The UV continuum of NGC 4151 decreased by a factor of 4 over the previous two years, and we argue the changes in the column density of the low ionization absorption lines associated with the broad component at -490 km/s reflect the decrease in the ionizing flux. Most of the strong absorption lines (e.g., N V, C IV, Si IV) from this component are saturated, but show substantial residual flux in their cores, indicating that the absorber does not fully cover the source of emission. Our interpretation is that the unocculted light is due to scattering by free electrons from an extended region, which reflects continuum, emission lines, and absorption lines. We have been able to constrain the densities for the kinematic components based on absorption lines from metastable states of C III and Fe II, and/or the ratios of ground and fine structure lines of O I,C II, and Si II. We have generated a set of photoionization models which match the ionic column densities for each component during the present low flux state and those seen in previous high flux states with the GHRS and STIS, confirming that the absorbers are photoionized and respond to the changes in the continuum flux. We have been able to map the relative radial positions of the absorbers, and find that the gas decreases in density with distance. None of the UV absorbers is of sufficiently large column density or high enough ionization state to account for the X-ray absorption.