The “Memory Function” is a more understandable term meaning toggle, rocker RS in our case. The concept of the RS flip-flops is shown in this tutorial.
The purpose of this arrangement is to introduce how to achieve another wired logic, ie with only the wire and core electrical components.
What should be done ?
In our assembly, this is the state of the lamp L which is stored (on or off):
To turn it on, simply press the ON button, and to turn it off, simply press the button OFF.
If you press both buttons simultaneously, the lamp goes off: it is said that the judgment has priority.
Saving is done through the special arrangement of the relay K and its contactor K1.
How does it work ?
By default, ON K1 is open: the current is blocked, so L is off.
When you press ON, the current can pass, so L is lit and the relay is active K, which closes contactor K1.
When ON is released, K1 is still closed, the current can continue to move in that K, still active, let K1 closed: the circuit remains closed L, therefore, remains on.
When OFF is pressed, the circuit opens: L goes off, K is no longer active and therefore K1 opens: Returning to the default situation.
Now you know make an RS flip-wired logic. This is not a better solution than the electronic logic or worse: you must choose one or the other depending on the type of circuit and imposed constraints.