What does the quote "Long Live the King" from the first scene in Hamlet mean?
This statement is Bernardo's answer to Francisco's challenge. Both are sentinels, standing guard outside the castle of the king of Denmark, and it seems that Bernardo is just signifying that he is a friend and not a foe. Of course, "Long live the king" is also a toast or a greeting, and it could also be that Shakespeare intended for the exchange to foreshadow, in an ironic way, the events involving the King of Denmark, Claudius, who has, we discover, gained the crown through the murder of his brother. But it is basically just a response to Francisco's challenge, similar to how Horatio identifies himself and Marcellus as "friends to this ground" later in the scene when challenged.