What is the use of R5, C4, C2, R6, R5, D1 in the below amplitude modulation circuit?
D1, R5, and C4 form an envelope detector.  You don't want L1 blinking on every individual cycle of the audio; you won't get the desired effect.  The intent of this circuit is that L1 change in brightness a little bit with every pronounced note, and a bit more for every beat.

With the envelope detector, the voltage driving L1 represents the shape of the audio, its peaks and valleys in loudness that occur with each note and with each beat.  How quickly L1 can respond to changes in the audio is set by the values of R5 and C4, called the time constant.  The longer the time constant, the less responsive the circuit will be to individual notes and the more responsive it will be to the beat and other large changes in audio.

EDIT: I just went out to the link.  Most Instructables circuits have problems ranging from frustrating to severe.  This one is severe.

The circuit cannot do what the text says it does.

The corner frequency of the envelope detector (basically, an asymmetrical  version of a low pass filter) is only 14 Hz.  So by the time you get up to human voice frequencies or the middle of a piano, the audio is attenuated by almost 30 dB.  That's a lot.  Separate from that, a solar cell has a very slow response time, basically another lowpass filter.

Separate from that, the input hipass filter attenuates everything below 1500 Hz.  Again, down at voice frequencies it is attenuating the audio by almost 12 dB.  And that is in addition to the envelope detector attenuation.

Overall, the circuit functions as a notch filter.  It passes very low and moderately high frequencies, but the stuff in the middle that makes up the vast majority of what we perceive as audio is greatly attenuated.

ak