but why would they do in this way
Because they are idiots and don't understand what they are doing.
and succeed?
They don't. This damages the Arduino input pin, it will fail after a time. It is also only half the Audio signal so is not much good for audio.
Are the resistors and capacitor used to make the audio signal into the range 0-5v?
No. The resistors bias the signal to the 2.5V mid point and the capacitor AC couples the signal so the resistors do not affect the DC component of the audio input.
I expect to read the analog value as 0-1023 (loudness)
No that is not what you will see. You see a reading of 512 for silence, the the louder it gets the further away the reading is, above and below, from this point. If you actually want readings like that then what you actually need is this circuit. It is called an envelope follower, use a capacitor to couple this circuit to your audio input.
Thank you for the circuit. I think it is the simplest one I have seen in these few days.
Hugh! It is the same circuit I pointed you at in reply #1.
But I found some circuits suggest using 0.47uF capacitor, what are the differences?
Slightly lower frequency response on the high pass filter this implements.
I am not very good at reading circuit diagrams, I would be appreciate if you could make me a simulation picture with the Arduino, breadboard and other electrical components,
No. That sort of layout diagram is an anathema to those here. If you want one make it yourself. Click on the schematic tab in Fritzing, copy the schematic, then click on the layout tab and drag your components round until everything is routed. That way you will actually learn something.