When the terminal voltage of the battery increases to 13.5 volts, pin 3 of IC2 gets higher voltage than pin2 and the output of IC2 becomes high. This activates the relay and the contacts break. Charging current to the battery cut off and the relay remains as such since the battery voltage(13.5V or more) keeps the voltage at pin3 of IC2 is higher than that of pin 2.
Charger Settings
Before connecting the battery, set the input voltage to IC2 using a fully charged battery or variable power supply. Turn the switch S1 to the off position and switch on the power. Then connect a fully charged battery/ variable power supply to test points TP observing polarity. Measure the input voltage to pin 3 of IC2.
Slowly adjust VR1 till the input voltage to pin 3 of IC2 raises to 5 volts. At this point, relay should energize and Red LED turns on. Then connect the battery for charging and switch on S1. If the battery takes charge, current to pin 3 of IC2 will be low since most of the current drain occurs into the battery. This keeps the relay off. When the battery voltage increases above 13.5 volts, no more current passes into the battery, so that the voltage at pin3 of IC2 rises and relay turns on.