John 19:19-24
John 19:19 (KJB)
And Pilate wrote a title, and put it on the cross. And the writing was, JESUS OF NAZARETH THE KING OF THE JEWS.
Since Pilate had nothing but disdain for the Jews, he made a sign which would have infuriated them. He placed a sign on the cross of Jesus designating Him as the King of the Jews and what made that saying worse was that he made sure that he wrote Jesus came from Nazareth. Nazareth, as you recall, did not have a good reputation so the Jews would have also loathed that part of the saying. The sign also signified the crime of the condemned. So Jesus was put to death for being a king, which would have pacified Rome’s requirement for a legitimate reason to crucify Jesus thus letting Pilate of the hook for abuse of power.
John 19:20 (KJB)
This title then read many of the Jews: for the place where Jesus was crucified was nigh to the city: and it was written in Hebrew, and Greek, and Latin.
Hebrew, Greek, and Latin were the three languages which were spoken of in Israel at that time. The site of the crucifixion was outside the main city of Jerusalem and it was probably to the north of the city walls. The reason that the sign was written in these three languages was so everyone in the city would understand and that fear of committing the same crime would be prevalent among the three language groups. This way Rome could keep the peace if the amount of malefactors were kept to a minimum.
John 19:21 (KJB)
Then said the chief priests of the Jews to Pilate, Write not, The King of the Jews; but that he said, I am King of the Jews.
The Chief Priests were vexed when they saw that sign and wanted it changed because they would not want Jesus as their king and they only saw Him as a blasphemer. If they did not like the title King of the Jews, then they should not have brought that false charge against Jesus in the presence of Pilate. What did they think that Pilate was going to do with the only accusation that he could possibly use to crucify Jesus? What else was Pilate going to put up there? Jesus of Nazareth, He healed the Sick, raised the dead, fed the multitudes? Pilate needed a legitimate crime to attach to the cross of Jesus and that was being a king which would be a threat to Rome’s power in the region.
John 19:22 (KJB)
Pilate answered, What I have written I have written.
The words “I have written” used both times are in the perfect tense in the Greek which means it was a permanent inscription and was not going to be changed. Pilate had acquiesced to their every demand by crucifying Jesus on such flimsy charges and no evidence at all for guilt. Here Pilate tells them that what he wrote will stand and he was probably very angry at this point and wanted nothing more to do with them.
John 19:23 (KJB)
Then the soldiers, when they had crucified Jesus, took his garments, and made four parts, to every soldier a part; and also his coat: now the coat was without seam, woven from the top throughout.
Garments - Cloak, robe
Once the soldiers had completed their tasks of crucifying the prisoners, they then went and shared whatever possessions they had amongst themselves. The first thing they did was to take the outer robe of Jesus and made it into four parts and each soldier took a part of that robe. The next piece of clothing they wanted to steal was the coat. The coat was like a shirt which covered the body from the neck to below the knees. This coat was sown seamless so they would not be able to part this garment.
John 19:24 (KJB)
They said therefore among themselves, Let us not rend it, but cast lots for it, whose it shall be: that the scripture might be fulfilled, which saith, They parted my raiment among them, and for my vesture they did cast lots. These things therefore the soldiers did.
Rend - To tear or split
(Psa 22:18 KJV) They part my garments among them, and cast lots upon my vesture.  The actions by these soldiers was a fulfillment of the prophecy in Psalm 22:18. Instead of them tearing the garment, they cast lots for the coat and only one would walk away with the coat of Jesus. Since it was seamless, it might have been a nice coat and was probably a gift from someone. It may have been a coat of higher quality or else why would the soldiers want it. If it was just an old coat, they would have probably just discarded it.