So in our circuit whenever the output at PIN 3 goes HIGH, the transistor starts working as an amplifier, and amplifies the current.
This current goes into the capacitor and charge the capacitor to the 2/3 Vcc (555 IC principal), at the same time LED glows.
After this, output at PIN 3 becomes low, transistor becomes OFF and capacitor start discharges through the collector-emitter junction. Capacitor discharges into the LED, which gives the LED fading effect.
As the capacitor discharges, LED illumination fades. Then again, PIN 3 goes high and capacitor charges and LED illuminates.
The led fading time is dependent on the resistors and capacitors value, if we increase the value of capacitor the LED would fade slowly. Like I have demonstrated in Video,