An arbitrary unit is like having a ruler without any numbers on it. It is a way of measuring something without using an exact standard. Sort of like saying "this pencil is longer than that pencil" but not knowing how many inches or centimeters either pencil actually is.
Scientists and researchers might use an arbitrary unit when they're studying something that doesn't have a well-defined measurement system. They might come up with their own way of measuring it using something that's convenient for them, like the brightness of a star or the loudness of a sound.
Because arbitrary units aren't standardized, they can be confusing for people who aren't familiar with the specific measurement being used.