At the end of Jesus' ministry, what did Jesus mean when He said "it is finished" (John 19:30)? Is this to be considered the end of Satan's Reign over humanity?
Yes, victory over Satan and over sin, for HE had accomplished what had been promised since the beginning with Adam and Eve: First Promise of the Savior?
Furthermore, note Jesus' prayer in John 17
“Father, the hour has come. Glorify Your Son, that Your Son also may glorify You, as You have given Him authority over all flesh, that He should give eternal life to as many as You have given Him. And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent. I have glorified You on the earth. I have finished the work which You have given Me to do. And now, O Father, glorify Me together with Yourself, with the glory which I had with You before the world was. (nkjv)
What is the work that God sent his Son our Savior to accomplish?
John 3:16-17 (nkjv)
For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. 17 For God did not send His Son into the world to condemn the world, but that the world through Him might be saved.
The death and resurrection of Jesus was the fulfillment of many prophecies (ex psalm 22), fulfillment of the Law (Matt 5:17), victory over Satan and sin, what ultimately ushered in the New Covenant, that is saved by grace through faith (ephesians 2:8), and I'm sure the list goes on.. :)
While agreeing heartily with Nick Rolando's answer, I believe there's at least one further, additional meaning: He also meant simply that His immediate work, i.e. the suffering on the cross, was finished.
A couple years ago for a Good Friday service, I and six other members of my congregation were asked to give brief messages on "the seven last words" of Jesus while on the cross. "It is finished" was the statement I was assigned. While praying about what to say & teach, I felt led to emphasize that Jesus was fully in control of the whole situation -- an important point to remember, and easily forgotten just because of the fact that was nailed to a cross!
So I likened the whole scene to a courtroom, with Jesus as the Sovereign Judge. It didn't matter that He had been stripped bare, it didn't matter that He was on the cross, it didn't matter that every person there saw only a condemned victim. He was still in charge, just as surely as if He were a judge in robes sitting at the bench. And so when He cried out "It is finished," He was bringing down the gavel and declaring the ransom paid and the court adjourned. Neither Pilate nor anyone else held that authority; it was Jesus' alone.
The gospels of Matthew, Mark and John all agree on one point; after Jesus had drank the vinegar, He cried out one last time, and then He died. John 19:30 gives us what He said: “It is finished.” The Greek corresponding to this is τετελεσται, tetelestai, the literal translation of which is “it has been accomplished.” Jesus, in His life and death, had fulfilled biblical prophesies of the suffering Messiah of Isaiah 53. In Him, the messianic prophesies had been confirmed, supported or upheld. According to Strong’s Concordance, the Hebrew verb אָמַן, aman, means to confirm or to support. It is the root word for “Amen.”
What Jesus meant by 'it is finished' are the things that were written for him to do. You can read that in Hebrews 10:7. All the things and prophecies about Christ, that he was able to finish, even his crucifixion mentioned by the prophets, were completed and done.
One example, was this prophecy about him, the Worm Jacob. Psalms 22:6.
It is finished. If you go to the original language. You will find that it also mirrors the business /accounting term "paid in full". Jesus had announced that He had come to "Fullfill the law ". Yes He could live the perfect life. But the part of the law no one could fullfill was the justice debt of death. Only blood covered the sin debt. And animal blood (life taken) was just a temporary symbol, as was most of what was in the OT. Of the realizations of the New Testament. And only the laying down of a perfectly lived life would suffice. Until that point there could be no possibility of a relationship with God. All of which is severely condensed and would take a while to dive into. But feel free to counter question. For teaching and learning are not opposites.