mmrassi, to clarify, what confuses you... The need to turn them off at all? Or why they should be turned back on (recycled)?
The recycle (turning back on) has been explained perfectly by 172_driver.
Why to turn them off to begin with, has partly been explained by Shiny side down. If using basic MCP modes, the guidance is no longer appropriate after reaching MDA (or when becoming visual) and should therefore be removed.
However, if you are flying non-precision approaches using LNAV/VNAV for flying the profile (with raw data checks in the background of course), you actually have sensible guidance untill the flare. In principle you could leave them on.
My guess is that that the requirement to turn them off (and then back on), is either to keep a uniform procedure whatever using LNAV/VNAV or basic modes. That and/or to relieve Boeing of responsibility from whatever you are doing below MDA.
Quite obviously the maneuver from MDA to landing should be accomplished visually. However, if going into a pitch black airport in the countryside with no moon and no visual cues otherwise, and using LNAV/VNAV, with a visually confirmed good guidance, I personally would postpone the recycle or leave it on altogether. I am a big fan of raw data and hand flying in general, but have a sound respect for darkness.