How does the iPhone Auto Focus work? How does the auto focus in the iPhone work?  Is there a something mechanical in there to adjust the lens or is it completely software?

Google provides this article which suggests some camera phones do have mechanical focus mechanisms.  I couldn't find anything specific to the iPhone however.
Autofocus on the iPhone is done via an electrical motor, moving the front lens backward and forward, and software that captures and analyses the image for best sharpness, which usually is the "sweet" spot. Recent versions of iOS probably offload the analysis to the image signal processor available since the Apple A5 chip.