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Pilate could see that the crowd was not going to back down and that things were getting out of hand. So he performed a public gesture: he washed his hands in front of everyone and said out loud that Jesus' death was not his fault. 'See ye to it' means 'that is your problem, not mine.' He was trying to put the blame on the crowd and walk away clean.

Pilate had tried to free Jesus by offering the crowd a choice between Jesus and a known criminal named Barabbas. The crowd chose Barabbas and kept demanding Jesus be crucified. Pilate found no good reason to execute Jesus, but the crowd was growing louder and more dangerous. This verse is the moment he gives up trying to stop it.

• Washing hands as a sign of innocence comes from Jewish practice (Deuteronomy 21:6-7), where elders washed their hands to say publicly they were not responsible for a death. Pilate borrowed that gesture here, likely knowing the crowd would understand exactly what it meant.
• Pilate calls Jesus 'this just person' — meaning an innocent man. He is saying out loud that he believes Jesus has done nothing wrong, even as he hands him over to be killed.

The gesture did not actually remove Pilate's responsibility. He had the authority to release Jesus and had already said Jesus was innocent. Washing his hands was a public statement, not a real transfer of guilt. He still gave the order.

Deuteronomy 21:6-7

In the Old Testament law, elders washed their hands over an unsolved murder to declare publicly they were not responsible for the blood. Pilate's gesture directly mirrors this ritual, which is why the Jewish crowd would have recognized it immediately.

Matthew 27:24

This scene is where the English expression “to wash your hands of something” comes from — to say publicly that something is not your fault.