There have been many many pages written on this question in the past and it can be answered on a number of levels.
Act 1 scene 1 is a fantastic example of scene-setting. The short prose lines, the staccato dialogue, the repetition of questions, the use of incomplete sentences and single word utterances wonderfully create an impression of fear and tension as the soldiers await the arrival of the Ghost. Unfocused statements of discomfort such as "I am sick at heart" anticipate the recurrence of this sensation as something is "rotten" in the state of Denmark which is an "unweeded garden".
The scene attracts and grabs the attention of a notoriously rowdy sixteenth century audience by starting in medias res, in the middle of something. It then relies on the sceptic Horatio to proceed and explain the setting and background to the audience: we are informed of the rebellion in Norway led by Fortinbras, the duel between old Hamlet and old Norway, the preparations for war.
The Act proceeds to introduce almost all the main concerns and themes of the play. Francisco's first question "Stand and unfold yourself" reveals the keen interest in the play to discover the truth that is often hidden behind layers of deceit. It recalls Hamlet's complaint that one may "smile and smile and be a villain", and his accusation to Ophelia that "God gave [women] one face and [they] paint another". The ambiguity about the ghost's authenticity is pursued throughout the play.
It introduces the character of the dead King Hamlet even before Hamlet's soliloquy identifies him with "Hyperion". We see him as a warrior King, combating the Pollacks and Norway; we see him as constantly legitimised in law in his duel with Norway. This clearly sets him up in conflict with and contrast to the "smiling damned" politician Claudius in scene 2 who deals with the threat from Fortinbras by diplomacy and not warfare.
There is so much in this scene which is wonderful and dramatic, not least the presence on the stage of the Ghost itself, a genuinely shocking moment for a sixteenth century audience. It would also have been very politically poignant: performed around 1600 when Elizabeth 1 was aged and there were serious concerns about the succession, the opening scenes detail a troubled and unsuccessful fictional succession.
Unfortunately, the character limits given here prevent me from developing the dramatic, linguisitc, political importance of the scene in any more detail. However, I hope the above gives you some ideas to think about.