Act I, Scene 1 of Julius Caesar creates the essential element of suspense in a drama and establishes several themes that will be developed later in the play, setting up the dramatic framework for what will follow.

First, it shows that the common people are very fond of Caesar and seemingly would not be opposed to his taking more power for himself. As the Cobbler says, "But indeed, sir, we make holiday, to see Caesar and to rejoice in his triumph."

Second, we are told that although the people are supportive of Caesar, they are very fickle and have previously supported Caesar's rivals with just as much fervor:

You blocks, you stones, you worse than senseless things!
O you hard hearts, you cruel men of Rome,
Knew you not Pompey? ....
And do you now put on your best attire?
And do you now cull out a holiday?
And do you now strew flowers in his way
That comes in triumph over Pompey's blood?

This raises a question mark over the popular enthusiasm for Caesar, and indicates that popular opinion may change if carefully shaped.

Third, in the words of Flavius and Marullus, the scene shows that some of the Roman ruling class have begun to entertain doubts and fears about Caesar's rise. These two officials explicitly charge the commoners with gross ingratitude, but they also indicate that they fear that unrestrained popular approval will go to Caesar's head and make him dream of still greater powers:

...let no images
Be hung with Caesar's trophies. I'll about,
And drive away the vulgar from the streets;
So do you too, where you perceive them thick.
These growing feathers pluck'd from Caesar's wing
Will make him fly an ordinary pitch,
Who else would soar above the view of men
And keep us all in servile fearfulness.

Thus, the first scene of Julius Caesar introduces the elements that Aristotle considered essential for the creation of suspense, an essential ingredient in drama. These are a looming danger, and a hope that the danger can be escaped or avoided. The unrestrained support of the commoners creates a danger that Caesar will use them to take supreme power, but their fickleness and the opposition manifested by some members of the upper class holds out the hope that this danger will be averted. Or, if we wish to take it from the other direction, the opposition of the upper classes and the fickleness of the commoners creates a danger that Caesar's ambitions will remain unfulfilled, but Caesar's own prowess and the support it has generated justify a hope that he will succeed in spite of all.

I would say that its dramatic significance or purpose is three-fold:

1. To set the play in time and place and introduce the character of Caesar through the opinions that common citizens have of him versus the opinions held by two Roman tribunes.  The purpose here is exposition.
2. It also serves to immediately involve the audience as "actors" in the performance.  Julius Caesar ,...