The Note to robert is received during the Ritual of the Mahjarrat quest. The note was written by Robert the Strong, and is addressed to himself. It contains information about the code to Kethsi (which is in Bob's collar) as well as some random information to prove to Robert that he wrote the note.
In the Note to you, Robert asks that you give him this note while he is human and not in his cat form, Bob the Jagex Cat. If you speak to Bob about the note, he has no interest in it.
Presumably, the note will have a use at some future time. Until then, for players wishing to save Bank space, the note can be destroyed, as it can be reobtained in Kethsi.