Antony's main point is to convince the plebians that Caesar was not ambitious, but rather he loved Rome and the Romans. By proving this, he would show that the conspirators acted out of spite and envy of Caesar, not from the standpoint of liberators.
He succeeds in doing this by giving several examples that show Caesar isn't ambitious, such as when he turned down the crown, when he cried for the poor, and when he used ransom money to fill the general coffers. At the end of the speech, he urges the plebians to riot and calls for Octavius Caesar. This foreshadows the war that will be the main conflict in Act V of the play.