Several major themes are introduced in Act I, scene I.
One theme in Hamlet is the return of the past, in this case the dead king. Throughout the play, old concerns return, the dead return, skulls turn up and are reflected on, etc.
Another theme is usurpation. When Horatio asks "What art though, that usurp'st this time of night," he's challenging the ghost, but he's foreshadowing the play's concern with Claudius' kingship.
And a third theme is that Hamlet must deal with all of this, and the scene ends by the guard deciding to drop it all on his shoulders.