Priority plane is for opacity ordering if you use alpha blend materials.
So priority "1" would always be rendered in front of 0 priority materials and so on.
For example if you overlay two blend materials you will get them randomly popping in front of each other, but not if you order them.
I think it does not work with cutout transparency though. (those are rendered just like normal modes)
I don't really know what constant color and sort far Z does but full resolution should force the model to always render the biggest mipmap regardless of how far it is.
Should is the keyword there since I think it doesn't really work.
All in all, I think those settings are relevant mostly for the UI elements.