In the Roman calendar, the 'Ides' referred to the middle of a month. The 'Ides of March' refers specifically to March 15th.
The soothsayer is a man who can apparently foretell the future, and he is warning Caesar to beware of the 15th of March. This is the day on which Caesar will be killed by a conspiracy of men who resent and fear his rise to supreme power. These conspirators include Marcus Brutus, who is Caesar's personal friend. Therefore, the soothsayer is right to warn Caesar, although he doesn't tell him exactly what is going to happen.
Caesar chooses to dismiss this warning, however. Although he does at first summon the soothsayer to him to hear what he has to say, he then remarks:
He is a dreamer. Let us leave him. Pass.
Caesar, then, dismisses the soothsayer merely as a 'dreamer', mistakenly believing that he has nothing important to say, and moves on with the procession. In fairness to Caesar, the soothsayer's warning is very vague, which makes it easier to ignore.
The soothsayer's warning ties in with other supernatural events that foretell Caesar's assassination: a fearful storm, ghosts and lions in the streets, and so on. Caesar's own wife, Calpurnia, has a terrible dream about him just before his assassination. All these signs point to the great political upheaval in Rome which will see the death of its most powerful figure, Caesar.
However, Caesar is arrogant and self-confident and chooses not to heed any signs or warnings, thereby making it easier for the conspirators to get at him. He is also anxious not to appear superstitious. However, if he had been more careful, he might have been able to save himself.
The Roman calendar used the word "Ides" to mean the end of a month. Ides usually came around the 15th. The fortune teller was saying that Caesar should be careful at the end of March. Caesar, however, ignored the warning from the fortune teller. As if by coincidence, Caesar was assassinated by his close friends on the Ides of March.