After learning that Jesus was indeed a Galilean, Pilate saw a way of escape from this difficult situation. He decided to send Jesus to Herod, since he also was in Jerusalem at that time and had jurisdiction over Galilee. This would either shift or divide the serious responsibility that had been placed upon him.
"Now when Herod saw Jesus, he was exceedingly glad; for he had desired for a long time to see Him, because he had heard many things about Him, and he hoped to see some miracle done by Him" (Luke 23:8; cf. 9:7-9). Jesus was nothing more than a curiosity to Herod. This ruler wanted Jesus to entertain him (like a court jester) with His divine power, but Jesus had no intentions of doing such. Herod was an adulterer and murderer, and he was the only man whom Jesus is ever recorded to have spoken a contemptuous word against (cf. 13:31,32).
"Then he questioned Him with many words, but He answered him nothing" - Jesus did not speak a word in Herod's presence. Our Lord did not answer any questions or deny any accusations. I believe Matthew 7:6 holds the key to understanding why.
"And the chief priests and scribes stood and vehemently accused Him" (Luke 23:10). The religious leaders felt that their "case" had failed before Pilate. Thus, they fervently continued to make their accusations against Him. What the Jews lacked in facts, they attempted to compensate for with their animated denunciations.
"Then Herod, with his men of war, treated Him with contempt and mocked Him, arrayed Him in a gorgeous robe, and sent Him back to Pilate" (Luke 23:11). Herod did not favorably receive Jesus' silence. He took vengeance upon Him through these abusive acts of contempt. However, since he could find no fault in Jesus, he returned Him to Pilate after much ridicule and humiliation.
"That very day Pilate and Herod became friends with each other, for previously they had been at enmity with each other" - Herod considered the fact that Pilate sent Jesus to him as a courtesy. It appears that Pilate had not always granted such courtesies (e.g., Luke 13:1), which may be why the two didn't get along to start with.
Although Herod was thankful for this opportunity, he was no help to Pilate. Pilate would have to deal with this situation himself. Such should not have been a difficult task since he had already determined that Jesus was innocent. It was simply a matter of letting Him go, and then dealing with the angry mob. That would have been the right thing for Pilate to do, but, sadly, he had no stomach for that course of action.