The soothsayer warns Caesar to beware the Ides of March, and Caesar ignores the warning.
The soothsayer supposedly knew that Caesar was in danger around February, 44 B.C. and made it his mission to warn him. In the play, Shakespeare has the soothsayer warn Caesar during the Feast of Lupercal. He tells him specifically when he will be killed.
Beware the ides of March.
He is a dreamer; let us leave him: pass. (Act 1, Scene 2)
Despite the specificity of the warning, Caesar ignores it. In either arrogance or distraction, he dismisses the man as a dreamer and tells him to go away. Caesar would have been well aware that he was a target for assassination. After all, he had just defeated another Roman in a bloody civil war and was taking more and more power for himself as dictator of Rome.
The soothsayer does not give up. He tries again on the Ides of March. Again, Caesar is not taking the warning seriously. He makes what seems like a joke when he sees the soothsayer.
[To the Soothsayer] The ides of March are come.
Ay, Caesar; but not gone. (Act 3, Scene 1)
The soothsayer has a point. Caesar is just about to go into the senate meeting where he will be assassinated. Again, he does not take precautions. He either feels that he is safe or does not care. Shakespeare presents Caesar as supremely arrogant, ignoring the Cimber brothers' requests.
If Caesar had listened to the soothsayer, history might have turned out quite differently. By the time Caesar faced his assassins, he had been warned by the soothsayer, Artemidorus, and his wife. He almost listened to his wife when she told him that, because of her dream, she did not want him to go but, unfortunately, he went there anyway.