Power filtering -- why, how, and how to "see it"

I have a question about power filtering.

It all started when I noticed that this product has it:

https://www.dfrobot.com/product-1493.html

It had three capacitors to perform some power filtering.
When I asked why, I was told that since this sensor is powered by a 5-12V wide voltage supply, they parallel several small capacitors between VCC and GND for power filtering.

So… questions:

1) What is power filtering exactly?

2) Why is it needed with wider voltage ranges?

3) How do the capacitors in parallel “filter” things?

4) (MOST IMPORTANT) Is there a way to simulate circuits online, and go as far as (a) Providing unfiltered “messy” voltage (b) "See the provided voltage in real time (c) Apply the small capacitors (d) See in real time how the voltage is filtered?

Thank you.