The Roman Empire was a very diverse place, and one of the efforts of the empire to create unity and promote the imperial administration was to establish the worship of the emperor as a deity. This became something of a state religion, and many official public rituals, celebrations, and even daily administrative tasks involved some kind of oath, swearing allegiance to ‘the Divine Augustus,’ or even just saying ‘Hail Caesar.’ There were also pagan sacrifices involved in some rituals.
It became the duty of every citizen to go once a year to a temple of Caesar, offer incense, and declare ‘Caesar is Lord.’ Romans were free to worship other gods as well, but if they refused to worship Caesar, it was seen as sedition, and even citizens could be sent to jail. Of course, most Christians openly refused to say that anyone was Lord except for Jesus. So, many were jailed, and some were even killed.