Meanings
In official documents and speeches, the use of the pronoun "we" by sovereigns or very high personalities means that they are not speaking as a private person, but almost interpreting the thoughts of those they represent.

Examples
The new principal uses the royal we while talking to the students. Maybe he thinks he's the new Pope
Il nuovo preside quando parla agli studenti usa sempre il noi del Plurale Majestatis: che si creda di essere il Papa

When you say "we are going on vacation" do you mean you and me, or are you only using the royal we?
Quando dici che "noi andremo in vacanza" vuol dire tu ed io, o stai solo usando il pluralis majestatis?"