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.