In this lab, in section "hardware section", it is written:
The current flowing through the diode, ID, is also the voltage measured across the resistor (100 Ω in this example)
Why? i just don't get it
Looking at figure 4, the answer is simple enough. The current supplied by the channel A generator can only flow through the resistor and the diode back to the ground connection. No current will flow in the channel B connection when it is in the high impedance mode. Ohms law tells us the the voltage across a resistor is equal to the current through the resistor times the resistance value.
The comment in that paragraph is there to simply point out (and reinforce) that the current in the diode can be found multiple ways. Either by direct measurement from the amp meter built into channel A or by calculation from the measured voltage.