In starting early on with this statement in his speech to the people, Mark Antony is stating that history is written by the victors. He is acknowledging that Brutus and his conspirators are the victors, having managed to kill Caesar. Brutus has just made a speech justifying the murder of Caesar by saying Caesar was too ambitious and that his ambitions threatened Rome.
Mark Antony states that in focusing on the evils Caesar may have done, his good deeds are forgotten (buried with him). Antony then goes to remind his listeners of some of those good deeds and uses them to question Brutus's version of what Caesar was like.
Antony asserts that Caesar's good deeds show him not to be ambitious. For example, he "wept" for the poor: Antony notes, too, that "ambition should be made of sterner stuff" than concern for the poor. Antony also points out that he offered three times to crown Caesar as monarch, thus planning to put a tremendous amount of power into his hands, but that Caesar turned him down.
Mark Antony is deeply upset over Caesar's death and wants to incite the crowd against Brutus and his followers by reminded them of all the good Caesar did.