Hi,
At the "dirty" path there are microcontrollers and other digital circuits. They cause the "dirt". They draw short spikes of current, causing high frequency noise. One time they draw more current next time they draw low current depending on code, this causes lower frequency noise.
The power supply will drift with load current, time and temperature. We can't prevent the power supply from drifting with time and temperature. But with the filter between dirty path and power supply we just reduce the high frequency influence of the digital noise. The low frequency noise will go back to the power supply.
Now to the "clean" path. It is fed from the power supply. The power supply is - due to the filter to the dirty path - more clean...and the filter to the clean path makes it more clean.
, I understand that clean means without any voltage fluctuations or variations
This you misunderstood.
It is by far not free from fluctuations. All the lower frequency fluctuations caused by temperature and time can't be filtered out and thus still remain.
But the higher frequency noise is attenuated. The ADCresult is more clean now... from sample to sample.
But if you do the same measurement now and an hour, a day, a year later ... it will still drift. Drift a lot.
The way of the HF dirt is: digital section --> filter --> power supply section --> filter --> analog section.
This describes just one source of noise. For sure there are many other. Like EMC caused noise, currents in the ground plane, power supply noise (SMPS) and many others ...
Klaus