Without a battery connected; nil happens, i.e. if the battery charging leads from the charger were shorted together no current will flow - this is an inherent safety feature.
Mains operation thru a step down transformer and full-wave bridge rectifier supplies voltage for charging the depleted battery.
With a 12 volt battery connected ; transistor T2 is biassed thru 4.7K resistor which switch's on T3 and hence applies a gating voltage to the SCR. With the SCR now in the conducting state current is delivered to the Battery (thru SCR).
As the battery is becoming charged-up its terminal voltage will increase gradually ( I have used the word asymptote here to describe this rate of rise of terminal voltage).
When the voltage reaches a point where the zener diode will conduct and switch on T1; this will rob base current from T2 and the SCR will no longer be triggered into conduction. This is essentially a high-voltage turnoff point.
This point is made adjustable by the potentiometer control (shown as voltage asymptote).
Operator variation of control will effectivley set charging current and may need adjusting up as the battery becomes more in the charged state.
Battery charging (traditionally should take about a 10 hr period - charge current reckoned at about 1/10th of the AHC (ampere-hour capacity).
If initially the battery terminal voltage is so low that charging will not commence then a start button will enable "on" the circuit electronics.
I have constructed many battery chargers to this design and find they work really well !