Hi,
the right bottom LM117 is a constant current source to get a constant voltage across the 150R pot.
Current = 1.25V / 120 Ohms = about 10.4mA (Iadj neglected)
The left top LM117 is the current limiter. The current measurement is the voltage drop across the 1Ohms resistor. (150 Ohms x 10.4mA = 1.56V)
And it is compared/regulated with the adjustable voltage drop of the pot.
With the wiper at the bottom there is about 1.56V between V_out and ADJ of the top regulator, it will not allow any load current to flow.
With the wiper at the top.. the the current will be limited to 1.25V/1Ohms = 1.25A.
Klaus