This is a simple 555-based circuit in which pressing the pushbutton next to the potentiometer drops the voltage on the trigger pin, turning on the LED for a single pulse.
Pressing the other pushbutton pulls the reset pin low, stopping the pulse.
The only thing I'm not sure about is why is the capacitor needed on the control pin. My book says it's necessary, but EveryCircuit does not seem to need it. Perhaps it's for isolating the control pin from noise in the digital ground?
