If you don't know what auto-bump is: auto-bump is a feature found in several other render engines, including Arnold and Vray. When this setting is enabled, the renderer figures out what additional detail could be created from the input dislacement map were the mesh subdivided further than current settings allow and renders that higher frequency detail as bump instead. This means that you can render with fewer subdivisions while still getting higher frequency detail and without having to manually workout some complicated scheme for doing so.
Arnold's documentation explains it this way:
Autobump puts the high frequencies of a displacement map into the bump attribute so that you do not need as many Subdivision Iteration values... When Autobump is enabled, Arnold makes a copy of all of the vertices of a mesh before displacement (let's call that the "reference" mesh, or Pref). Prior to shading at some surface point on the displaced surface P, the equivalent Pref for that point is found on the non-displaced surface, and the displacement shader is evaluated there (at Pref) to estimate what would be the equivalent normal at P if we had subdivided the polymesh at an insanely high tessellation rate.
