What is Harry?

Harry is the new King, thirty for and ignorant to all that the status entails.

What does that do?

Gives Harry an infallible social status allowing him to do whatever he likes, causing my favorite scene. When Aumerle is forced to borrow someones Gage in order to throw to the ground because he is out and still very disgusted and has to challenge someone else.

What does that mean?

It means Harry is the judge of Richards fate and the fate of all England.

What is Richard?

Richards throne is usurped, he is in emotional turmoil I imagine terrified for his life.

What does that do?

What it does is sets Richard on the same lowly level as those around him, meaning he is subject to the commands of another something he had never experienced.

What does that mean?

It means Richard has finally become a human and Harry has ascended beyond it, both breaking the "Natural order."