What political events do Horatio and the guards link to the strange appearance of Old Hamlet's ghost?
HORATIO: As thou art to thyself.
Such was the very armour he had on
When he the ambitious Norway combated.
So frown'd he once when, in an angry parle,(75)
He smote the sledded Polacks on the ice.
'tis strange. (I.i.)
Upon the appearance of Hamlet's Ghost, Horatio notes that the apparition, which looks very like the late King of Denmark, is clad in the armor he wore in a battle with the Norwegian army. Also the ghost is wearing an expression which is similar to one the King, while alive, had when victorious over the Polish army in a battle on the ice. These are important clues to what the appearance of the ghost may mean to Horatio and the guards.
HORATIO: ...Now, sir, young Fortinbras,
Of unimproved metal hot and full,(110)
Hath in the skirts of Norway here and there,
Shark'd up a list of lawless resolutes,
For food and diet to some enterprise
That hath a stomach in't; which is no other—
As it doth well appear unto our state—(115)
But to recover of us, by strong hand
And terms compulsatory, those foresaid lands
So by his father lost. And this, I take it,
Is the main motive of our preparations,
The source of this our watch and the chief head(120)
Of this post-haste and romage in the land.
Horatio explains to the guard the circumstances of the last wars between Old Fortinbras of Norway and the old (now dead) King Hamlet. Hamlet had won from Norway certain lands that, in an agreement before the battle, were to be held absolutely by whoever won the battle. Hamlet won, and Fortinbras died in the battle. So Hamlet gained those lands under the treaty, and died possessing them. Young Fortinbras, the new king of Norway, wants to take back those lands by force. He is arming himself and mustering an army, so great preparations for war are going on in Denmark to defend the lands they won in the last war. Later in the scene the guards hope to learn the outcome of the battle between Denmark and Norway; in this time ghosts were sometimes believed to be portents of future events, and were sent to the world in order to warn people of things that were going to happen. The "warlike form" (I.i.58) of the ghost further convinces the guards and Horatio that the meaning of his appearance is related to these events.