"Punctuality is the politeness of kings."

This article explains it rather well:

Kings (especially before the [French] revolution) didn’t need to be punctual. They could show up when they wanted. Afterall, people would wait for them. But [King Louis XVIII of France, to whom the quote is often attributed] suggests that one way a king can show respect for other people is to meet them at the appointed time. If this is true for kings, it certainly is true for you and me. [emphasis added]

I could not find any explanation, just attributions to Louis XVIII, but my educated guess is this: Kings are not beholden to do much in the way of politeness (open doors, wait for others to be seated, etc.). However, to be punctual, treating other people's time as valuable as his own, is one way that a king can show politeness.

Being punctual is one of the most important qualities for a king as he has no other way to show politeness as in standing up to greet his subjects. Kings should be punctual to show that they want to be polite to everyone present at the court, be it the poorest of the poor man. If a great king can be punctual, so can you and me. After all a stitch in time saves nine.