The MOC3051 Series consists of a GaAs infrared LED optically coupled to a non–Zero–crossing silicon bilateral AC switch (triac)
 
The internal IR LED is connected between pin 1 and pin 2. The voltage source Vcc should be able to provide 15mA through resistor Rin to the Anode pin of the LED. The NAND gate connects the Cathode pin of the LED to ground based on a PWM signal from the microcontroller.  So one input pin of NAND gate will be connected to ground while the other is connected to the PWM signal.
Based on the PWM signal the LED will be turned on at particular interval for which the internal TRIAC will also be turned on. When the internal TRIAC is turned on it switches the external TRIAC which in turn controls the AC load. The 39 ohms Resistor and the 0.01uF capacitors forma an optional Snubber circuit. Thus based on the duty cycle of the PWM the output voltage will also vary which enables us the control the speed of intensity of the load.
 
Applications
AC Light dimmers
Contactor / Relay Control
AC motor speed control
Noise coupling circuits
Controlling AC loads using MCU/MPU
Ac/DC Power control
Solenoid / Valve control 
 
Resources: 
1. Datasheet