Shakespeare needed a group of extras for the pivotal scene in which Antony turns the mob against Brutus, Cassius and the other assassins. Since Shakespeare had to pay these extras, he probably wrote in a couple of additional scenes in which he could make additional use of them. So in the opening scene he has a group of plebeians wandering rather aimlessly about the streets of Rome until they are confronted by the two tribunes. Then after the mob riots there is a scene in which some of them encounter Cinna the poet and ultimately tear him to pieces under the misapprehension that he is the Cinna who is one of the conspirators. Both of these scenes would probably not have been included in the play if Shakespeare had not needed a fairly large group of extras to serve as the audience at the speech made by Brutus explaining the reasons for Caesar's assassination and then as the audience at Antony's famous funeral oration and the rioters they became under his influence.
The plebeians act as the audience for the histrionics of Julius Caesar in Act I and for the persuasive rhetoric of Brutus and of Marc Antony in Act III. Swayed dramatically by Antony, they rush into the streets, rioting. As a result, a civil war begins, a war that devastated Rome. Thus, Antony proves himself a hypocrite in declaring love for Rome. This mark upon his character is later underscored by his treatment of his nephew, whose life he gladly trades in Act IV.
They are easily swayed, veering from supporting one character to the next after Caesar's murder. After the death of Caesar, for example they hail Brutus as a hero. Then Antony's speech, while ostensibly only done to "bury Caesar," persuades them to support him, and they run riot in the city, chasing the conspirators into exile. So they are the force behind the actions of these men, and they are very easily harnessed in support of one man or another. A bit of a cynical view of urban crowds, but it does leave us asking who is supposed to be the "good guy" in the play, which is one of its many qualities.
Thank you very much ^-^