The Recent Evolution of the Dwarf Starburst Galaxy NGC 625 from Hubble Space Telescope Imaging

New HST/WFPC2 imaging of the dwarf starburst galaxy NGC 625 is presented. These data, 80% complete to V and I magnitudes of 26.0 and 25.3, respectively, allow us to study the recent star formation history of NGC 625. We derive a tip of the red giant branch (TRGB) distance modulus of 27.95+/-0.07, corresponding to a distance of 3.89+/-0.22 Mpc, and a location on the far side of the Sculptor Group. NGC 625 has a well-defined radial stellar population gradient, evidenced by a central concentration of young MS stars and an RGB/AGB ratio that increases with galactocentric distance. The prominent AGB is very red, and RGB stars are detected far from the central star forming regions. Using H Alpha and H Beta narrow band imaging and previous optical spectroscopy we identify substantial and varying internal extinction (A_V = 0.0 to 0.6 mag) associated with the central active star formation regions. To better understand the effects of internal extinction on the analysis of young stellar populations, synthetic models are presented which, for the first time, examine and account for this effect. Using the luminous blue helium burning stars, we construct a simple model of the recent (< 100 Myr) star formation in which an elevated but declining star formation rate has been present over this entire period. This is at odds with the presence of spectroscopic W-R features in the major star formation region which imply a short duration (<= 5 Myr) for the recent starburst. This suggests that starbursts displaying W-R features are not necessarily all of a short duration. Finally, we speculate on the possible causes of the present burst of star formation in this apparently isolated galaxy, and compare it to other nearby, well-studied dwarf starburst systems.