Need help explaining assigning attribute for graphic card with nvidia-settings

This is the attribute format in nvidia-settings’s manual pages

{DISPLAY}/{attribute name}[{display devices}]={value}

This is what I’ve always been using (copied from guides and it works)

[gpu:0]/GPUGraphicsClockOffset[3]=200

I’m not quite understand {DISPLAY} and [{display devices}] of which equivalent in realtime usages are [gpu:0] and [3]
respectively. As far as I know, DISPLAY is a collection of screen, why a DEVICE is in its place? And what is the number [3] ??

In your example the first index represents the numbering of physical NVIDIA GPUs in the system because NVIDIA GPUs work fine without the X.org server running.

The second index refers to performance level 3.

You can query performance levels by running:

nvidia-settings --query GPUPerfModes

You might want to reread manuals because all this information is in there.