The play takes place in ancient Rome, just after Julius Caesar has defeated Pompey and his sons and returned to Rome in triumph. (FYI – Pompey was a former co-ruler in the first Roman triumvirate, or rule of three men.) Though it's not spelled out in the play, Caesar's power is growing. He's been elected Consul (the highest office of the Roman Republic) for life, giving him unprecedented power. Though a lot of the actual events are crunched together for Shakespeare's literary purposes, the general feeling is that it's a time when Romans are happy to be recovering from civil war – so happy that they don't worry that the Republic is in danger of becoming an empire led by one king instead of elected representatives.
To give you a little context, Caesar was actually assassinated on March 15, 44 B.C., and Antony's alliance with Octavius in the second triumvirate came to an end eleven years later, in 33 B.C., when a disagreement turned into a war. Power politics were beginning to become the norm in Rome, and Rome's honor and tradition as a republic hung in the balance.