Using a combination of vertical transport measurements across and lateral transport measurements along the LaAlO$_{3}$/SrTiO$_{3}$ heterointerface, we demonstrate that significant potential barrier lowering and band bending are the cause of interfacial metallicity. Barrier lowering and enhanced band bending extends over 2.5 nm into LaAlO$_{3}$ as well as SrTiO$_{3}$. We explain origins of high-temperature carrier saturation, lower carrier concentration, and higher mobility in the sample with the thinnest LaAlO$_{3}$ film on a SrTiO$_{3}$ substrate. Lateral transport results suggest that parasitic interface scattering centers limit the low-temperature lateral electron mobility of the metallic channel.