What does the I.N.R.I. on the top of our crucifixes mean?

It is an abbreviation for Jesus Nazarenus, Rex Judeorum – Jesus of Nazareth, King of the Jews. In Latin the “I” and “J” are usually interchangeable and ancient Latin did not use the “J”. That is why it is INRI not JNRJ. 
 
It was common for the Romans to hang a “titulus” or sign above the crucified to indicate the charges against him. Scripture says that Pilate put the charges in Latin, Greek and Hebrew. 
 
Pilate placed this title above Jesus in scorn and mockery rather than faith. He also likely knew it would irritate the Jewish leaders, which it did (see Jn 19:21). 
 
Yet even in his ridicule, Pilate spoke truth. Jesus is King, not of the Jews only, but of all things.