What does I.N.R.I. on the crucifix mean?

I.N.R.I. is the abbreviation for the Latin phrase, Iesus Nazarenus Rex Iudaeorum

That is "Jesus of Nazareth, the King of the Jews". 

Remember after Jesus was crucified, Pontius Pilate wrote that and fastened on top of his cross in Latin, Greek and Hebrew. The Bible tells us that when the Jews noticed this, they asked Pilate to change it and he insisted that what he has written remains written. It is abbreviated because writing it in full may not be as visible as it is. John 19:19-22