In two of Rabbi Reisman’s shiurim, citing Rabbi Isaac Sher as the source, he develops the theme of what it means to establish a relationship with Hashem as our King.  The following is a summary of his discussion.  

Rosh Hashana is the day that we proclaim Hashem as our King.  Elul is the time of preparation for Rosh Hashana.  Yet Elul emphasizes an intimate relationship with Hashem—ani l’dodi v’dodi li, not what one thinks of when thinking about a subject’s relationship to his King.  But it is precisely this close relationship to our King that we are trying to capture.

The justice meted out by a court of law, a bais din, is straightforward.  If someone steals something, there is a specified punishment.  It does not matter who the individual is, or whether he stole to feed his family, or because he hated the individual from whom he stole.  The same punishment applies.  However, the justice dispensed by a king is different.  A king can take into account special considerations and can override the rule that a beis din would give.  An example of a king giving a harsher judgment is illustrated by the story of Nasan Hanavi reprimanding King David after he took Batsheva.  Nasan tells David a parable of a poor man with one sheep and a rich man who has many flocks.  When the rich man wants to make a banquet for his friends, he takes the poor man’s sheep and kills it, rather than one of his own sheep.  Nasan asks David (the king) what the judgment should be against the rich man.  David replies that he deserves to die.  Death is obviously not the prescribed punishment for stealing and killing a sheep.  But David took the circumstances into account to give a harsher judgment.  We have an example of Hashem, as King, giving a kinder judgment when the Heavenly Court (beis din shel ma’alah) would not accept an evil king’s teshuva, but Hashem made a tunnel, as it were, under the Heavenly Court to allow the teshuva to be accepted.  So, a king can take his personal relationship with the individual into account.