You can turn AC into DC with diodes. Unlike the half-wave rectifier, which only lets the positive part of the AC cycle power the load, a full-wave rectifier uses both halves of the cycle. It's also called a bridge rectifier. Normally you wouldn't use LEDs in the bridge part of this circuit, but it matches the lecture note colouring. The load is a blue LED and resistor to set the LED current. The source voltage is 120 V_rms @ 60 Hz, like a standard North American wall outlet.
The two red LEDs conduct for the positive half of the cycle, and the two green LEDs conduct for the negative half. They route the current through the load in the same direction both times. You can reduce the ripple by closing the switch to add a large "bulk decoupling capacitor" to smooth out the voltage (it stores charge when the rectified source voltage is high and powers the load when the voltage drops - like a charge gas tank).