From the Super Mario Wiki
Richard Burbage was an actor during the Elizabethan era. He was a part of the Lord Chamberlain's Men troupe, which worked closely alongside William Shakespeare and acted out many of his plays. In Mario's Time Machine, in 1601 at Stratford-upon-Avon, he was preparing for Shakespeare's newest play, Hamlet, where he was to take the role of the protagonist, Prince Hamlet. At this point, he meets Mario, who traveled back in time to return the Skull that is being used for this production of Hamlet.
Mario's Time Machine
When Mario first meets Richard in Stratford, he attempts to introduce himself, but Richard then interrupts him by saying that he is a great actor, giving his name, and boasting that he can work with any script. As he boasts about being a part of the Lord Chamberlain's Men, he proceeds to quote Prince Hamlet teaching some actors: "We hold, as ‘twere, the mirror up to nature, reflecting this stuff called life."* Mario is confused by this, and Richard explains that it refers to how life is complicated to understand, let alone explain. He then proceeds to quote As You Like It: "All the world’s a stage, and all the men and women merely players." (2.7.146-147) Mario asks him how many plays Shakespeare has written, with "some 24," (despite there being thirty-six plays in Shakespeare's First Folio, and only eighteen of them were published earlier) including comedies, tragedies, and histories. Mario is impressed by Shakespeare's bibliography, and Richard also praises him, describing him as one of the best playwrights in English literature and a good actor. He then remembers that he has Anne Hathaway's Knife and tells Mario to bring it to her. Mario then asks him if he should be rehearsing, and he suddenly remembers that he needs to be practicing for his role of Prince Hamlet and that he needs a feather to complete his costume. After Mario obtains the Feather from Anne and gives to to Richard, he proclaims that his costume is complete and continues to quote Hamlet, although he does not quote Prince Hamlet: "This above all: to thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man!" (1.3.79-82) Mario does not understand it at all, and Richard explains that if one is able to be honest with themselves, they are able to show their honesty to others. He then mentions that the Globe Theatre is in need of a sign to attract customers. Mario then gives him a Globe, and he gladly he takes. He finally bids Mario farewell as he leaves to prepare for his performance.
* - The quote is actually, "for any thing so overdone is / from the purpose of playing, whose end, both at the / first and now, was and is, to hold, as 'twere, the / mirror up to nature; to show virtue her own feature, / scorn her own image, and the very age and body of / the time his form and pressure." (3.2.20-25)