U1 pin 5 is connected to one of the internal reference voltage divider taps and C4 filters this point to reduce effects of noise on the power supply. Test point TP1 provides a reference voltage for calibration purposes that can be compared to TP2 (adjust ON Adj so that TP2=TP1) and TP3 (adjust OFF Adj so that TP3=0.5 x TP1).
U1 output pin 3 will have a low voltage when the circuit is "ON" and a high (near VCC) when it has tripped off. Q1 inverts this action so that the "ON" state is high. Q1 and R11 also level shifts the high voltage state to the 10-14 volt supply level rather than the regulated VCC. This reduces the current required from the regulated supply.
CR1 is a protection diode to prevent excessive current flow through the MosFET relay driver if the battery voltage should be reversed.
Q2 is the relay driver. An N-channel power MosFET is the best for this purpose since it requires no current to turn on (only voltage) and can switch considerable power at modest cost. There are alternative relay drivers using NPN single and darlington pair transistors shown below as options. It is also possible to use P-Channel MosFETs as direct "high side switches" in place of the relays. However relays will have the lowest voltage drop (virtually zero) whereas MosFETs have an inherent series resistance RDS that will combine with the current to give a very significant voltage drop. For more details, see the High Side options below.
CR2 protects the circuitry from the reverse spikes that relays generate when they turn off. The relay K1 must be chosen with several factors in mind. You want minimum coil current to conserve power but the relay contacts must be able to handle more than the maximum current that your equipment will draw from the batteries. See "Relay Selection" below. A simple modification to the relay can substantially reduce the current required to hold the relay closed.
A high resolution GIF image of the schematic can be viewed but it may not show or print too well on most browsers. I would recommend that you save it as a file and load it into a bitmap viewer such as PaintShop and print it out from there.