Arguably Caesar’s most well-known quote, “veni, vidi, vici” is just another example of Caesar’s superb statesmanship.
One could argue that a good knowledge of PR was the most important skill a Roman politician had to master, seeing as they needed the votes of the people to obtain power. (Whether or not they obtained these votes without bribing the people is another discussion, and such a thing was commonplace, if not legal, in ancient Rome.)
Caesar was perhaps the best Roman statesman throughout Ancient Roman period, as seen by his accomplishments in political and social reform during his period as consul and, later, dictator of Rome. Caesar knew how to form strong bonds with the people and maintain them. The best way to do this while he was away on campaign was to write letters back to Rome, letting the public know what he was doing and informing them of the battles he won for Rome. Doing this, he assured his people that he was off fighting (and winning, for the Romans only cared for a general that won his battles), for the glory of Rome.
While Caesar was away, his legions came under attack from Pharnaces II of Pontus in what is known as the Battle of Zela. After managing to rally his legions and defeat the enemy army after they took Caesar by surprise, Caesar writes his iconic “catch-phrase” of “veni, vidi,vici”, in a letter back to Rome.
This let the Roman people believe that Caesar won a quick and decisive victory in his short war against Pontus, implying Caesar’s great ability as a general.
So, to summarise, Caesar used this phrase to imply a short and decisive victory to inform the Roman people that he was still winning battles quickly and effectively for the glory of Rome for the purpose of keeping a good relation with the Roman people who would later vote him into political power.