There are 2 meanings of the word, "arbitrary".
The first meaning states that this word defines something to be random and based on personal whim or choice, not something that is frequently occurring. There is no specific reason or system for this particular course of action. Just like how the rain does not conform to the schedule or timing as predicted by the weather forecast, it is completely by chance thus it is an "arbitrary rain".
Perhaps the choice you need to make is erratic or very sudden, thereby not complying with carefully-thought out procedures, thus making it an "arbitrary decision".
Next, the word could also mean an unrestrained and autocratic rule of power or authority. For instance, we could say that the totalitarian rule of North Korean president Kim is arbitrary when sending citizens to be executed merely by defaming his name and reputation.
