When the battery voltage is below 13.8V, the voltage at TP1 will be lower than 7.2V. Therefore the output of IC1 will switch low, drawing current through LED1 and its series 100W and 1kW resistors and thus providing forward bias for Q1. Q1 switches on, allowing charging current to flow into the battery.
As soon as the battery terminal voltage rises to 13.8V (or the preset voltage), TP1 rises above 7.2V and this causes the output of IC1 to switch high. The current through LED1 falls to zero and Q1 is switched off, preventing any further charging. The 47kW resistor between pins 2 & 7 of IC1 provides about 0.5V of hysteresis so that the battery voltage will need to drop by 500mV or so, before the circuit can turn back on to provide more charge.
Zener diodes ZD1 and ZD4 together with the 22W resistor are added to prevent over-voltage damage to either IC1 or Q1.