The Romans sometimes forced their victims to wear a titulum when convicted of a crime. The titulum or "title" brought shame to the criminal as it announced to the public his crime. This titulum could then be affixed to the victim's crucifix as a warning to other would-be criminals.
The Gospels record that Pontius Pilate issued Jesus a rather sarcastic titulum reading "Jesus of Nazareth, King of the Jews" in three languages: Latin, Greek, and Hebrew (likely Aramaic).
The priests objected to the titulum and asked that it be rewritten to read: "This man claimed to be the King of the Jews" but Pilate answered, "I have written what I have written." (Jn 19:22)
Perhaps Pilate wished to send a message to the Jewish population that anyone else claiming regency in Judea was likewise be crucified.
The "I.R.N.I." is an artistic rendering of the title in Latin: Iesus Nazarenus Rex Iudaeorum ("Jesus of Nazareth King of the Jews").