Initially, Shakespeare characterizes Richard II through the address Bolingbroke and Mowbray make to him:
First, the fair reverence of your highness curbs me
From giving reins and spurs to my free speech;
They use figures of speech of several sorts when addressing him. Their address to him is offset by the remarks they make about others.
In this quote, the figure of speech called metonymy is used when Richard II is addressed as "highness." This is not literal (he is not "high up") but a representative way to refer to Richard's importance and order in hierarchy of authority: he is high in the hierarchy.
"Reins and spurs" is an idiom mean unmitigated, unsoftened speech: Richard's high position of goodness causes Mowbray to soften his tone and words so as not to offend Richard's high position of goodness.