In general, we understand synecdoche to mean the part standing for the whole.

In Antony's speech praising Caesar and subtly (or not so subtly) condemning Brutus and the other assassins in act 3, scene 2, Antony uses the literary device of synecdoche from the start. This shows from his first words that he is a master orator.

After addressing the crowd in flattering terms, he begins with "lend me your ears." This is a synecdoche. Antony doesn't literally want the listeners to detach and loan him their ears. He uses "ears," the part, to stand in for the whole: what he means is "pay close attention to the real meaning of what I am going to say." This is a memorable phrase that sticks in the mind in the way, say, "listen up," would not.

Further, when he holds up Caesar's bloody robe, and shows it ripped in the places where the assassin's swords went through to stab him, the robe stands for the murdered Caesar himself. This is a very effective synecdoche for Caesar's body and stirs up the crowd to anger against Brutus and his followers for their violent treachery.

Act III Scene 1 –

“Let each man render me his bloody hand”

Here, a hand (or handshake) stands for the whole loyalty of the citizen(and this is followed byseveral other mentions of “hands” to mean “your strength, your support” etc.) Example:“Woe to the hand that shed this costly blood!”

 In Antony's famous funeral speech: “I thrice presented him a kingly crown” is meant to mean he was offered the whole empire, but refused it, and “My heart is in the coffin there with Caesar” means his whole love is with Caesar.

In a larger sense, Caesar’s body is synecdoche for the man as a ruler and as a man.  And the people who hear the speech stand for the entire Roman citizenry.

There are other examples of this figure of speech, also: "sword" for soldierly strength, etc.  "  "Dip their napkins in his sacred blood" "Caesar's will", etc.