I got it wrong above. I've now run a sim of the circuit. With the component values as shown, IC2a,b never change state, regardless of battery/supply voltage, so do nothing useful !!
However, if R20 is changed from 5k1 to something like 200k it all begins to make sense. On the 12V setting, IC2a,b outputs then stay low if the battery voltage is below ~13.2V, i.e. the charging will only turn 'on' when the battery voltage is >13.2. Charging will continue until the battery voltage reaches ~14.4V, at which point IC1a,b,c trip and turn the charging 'off'. These figures are consistent with the ON/OFF figures shown just below the title of the schematic (a bit of a clue there
). Similarly consistent (more or less) figures are obtained on the 6V setting.
So, in summary, it looks like IC2 does the 'ON' voltage check and IC1 does the 'OFF'. It also seems the circuit will refuse to charge a very flat battery.
If you've got LTspice, here's the .asc file to play with. If you haven't, then I recommend you get it (it's a free download from Linear Technology and /or the Yahoo LTspice User Group).