We present Hubble Space Telescope WFPC2 images of elephant trunks in the H II region M16. There are three principle results of this study. First, the morphology and stratified ionization structure of the interface between the dense molecular material and the interior of the H II region is well understood in terms of photoionization of a photoevaporative flow. Photoionization models of an empirical density profile capture the essential features of the observations, including the extremely localized region of [S II] emission at the interface and the observed offset between emission peaks in lower and higher ionization lines. The details of this structure are found to be a sensitive function both of the density profile of the interface and of the shape of the ionizing continuum. Interpretation of the interaction of the photoevaporative flow with gas in the interior of the nebula supports the view that much of the emission from H II regions may arise in such flows. Photoionization of photoevaporative flows may provide a useful paradigm for interpreting a wide range of observations of H II regions. Second, we report the discovery of a population of small cometary globules that are being uncovered as the main bodies of the elephant trunks are dispersed. Several lines of evidence connect these globules to ongoing star formation, including the association of a number of globules with stellar objects seen in IR images of M16 or in the continuum HST images themselves. We refer to these structures as evaporating gaseous globules, or "EGGs." These appear to be the same type of object as the nebular condensations seen previously in M42. The primary difference between the two cases is that in M16 we are seeing the objects from the side, while in M42 the objects are seen more nearly face-on against the backdrop of the ionized face of the molecular cloud. We find that the "evaporating globule" interpretation naturally accounts for the properties of objects in both nebulae, while avoiding serious difficulties with the competing "evaporating disk" model previously applied to the objects in M42. More generally, we find that disk-like structures are relatively rare in either nebula. Third, the data indicate that photoevaporation may have uncovered many EGGs while the stellar objects in them were still accreting mass, thereby freezing the mass distribution of the protostars at an early stage in their evolution. We conclude that the masses of stars in the cluster environment in M16 are generally determined not by the onset of stellar winds, as in more isolated regions of star formation, but rather by disruption of the star forming environment by the nearby 0 stars.