What is Arbitrary unit?

Answer 1

Arbitrary unit means that you cannot calibrate your equipment and therefore you cannot tell us how your data compares to other data. "Arbitrary" means you produced it, and it's unofficial.

In other words, if you walk in the mountains, and you measure your distance with a stick, then, as a scientist, you'd write "the distance was 5000 au", because you're not going to tell us about your stick, as we don't care.

Or a more serious example: imagine you're looking at a cell through a microscope, and would like to say how big the cell is, but you don't have a scale in milimeters. Then you could put a small object, let's call it a "red ball" next to the cell, and when you say "my cell was two red balls wide", then you're using your arbitrary unit of "red ball".

Mainly Arbitrary unit is used for in measuring the light intensity.