What was Jesus referring to when He said "it is finished"? What is "it" in this case? 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.. :)