French hôpital ambulant, the mobile field hospital that marched with Napoleon's armies, shortened to ambulance by the Crimean era. Latin ambulare (to walk, travel) underlies it: the unit's defining feature was mobility, treating wounded near the front instead of waiting for transport back.
The word's family still strolls: amble, preamble (walking before), perambulator (the pram, for walking babies), somnambulist (sleepwalker). The ambulance is the one family member in a hurry, the walking word that learned to sprint.
Ambulare's PIE ancestry is foggy, possibly tied to wandering roots that also surface in aberration. The deep pattern: Latin measured civilization by movement, roads, marches, itineraries, and the ambulance inherits an empire's assumption that help, like legions, must travel to you.
How did the slowest word get the fastest vehicle?