The guards all think the ghost looks suspiciously like the recently deceased King of Denmark, especially around the eyes. Everyone tells Horatio to talk to the ghost, since he's the scholar in the group (turns out, he's not a guard).
Horatio asks the ghost a few questions which are apparently offensive, as the ghost walks off without answering.
To further confirm that the ghost is the image of the dead King, Horatio remarks that it was wearing the same armor the King wore when fighting Norway. Everyone's got a bad feeling about this, and to try to make sense of it, Marcellus asks Horatio for a little history lesson.
We learn that, a while back, Old King Hamlet made a little wager with the King of Norway about who could kill the other person first in combat. Gee, that sounds safe.
Old King Hamlet won so he got to take a bunch of Norway's land. The king of Norway's son, young Fortinbras, has raised an army to get his family's land back.
He also wants revenge for his dad's death, naturally.
Hm, we're already sensing a theme.
Because the kingdom of Denmark is preparing for war with Norway, Horatio's number one concern is that a dead man walking about in ghost form might be a sign that Denmark is going to lose.
Horatio is busy detailing just how bad an omen this is, with many references to Julius Caesar's death and all the nasty things that came before it, when the ghost comes back.
The guards want the ghost to stay and speak, so they try to hit it to make it stand still. Unfortunately, they can't really keep it in their sights long enough to land any blows.
Then they rehash events: (1) they were silly for trying to strike at the ghost, and (2) the ghost was probably going to say something, except the cock crowed and scared it off.
Horatio suggests they tell Prince Hamlet about the ghost that looks an awful lot like his father. Maybe Hamlet will know what to do, because these guys sure don't.