Ephesians 2:1-3 And you He made alive, who were dead in trespasses and sins, 2 in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience, 3 among whom also we all once conducted ourselves in the lusts of our flesh, fulfilling the desires of the flesh and of the mind, and were by nature children of wrath, just as the others.
Let's consider a few other passages for context and then come back to Ephesians 2.
John 12:31-33 Now is the judgment of this world; now the ruler of this world will be cast out. 32 And I, if I am lifted up from the earth, will draw all peoples to Myself." 33 This He said, signifying by what death He would die.
What would be cast out? By means of Jesus' death, "the prince of this world" would be cast out.
Hebrews 2:14 Inasmuch then as the children have partaken of flesh and blood, He himself likewise shared in the same (same nature - RSV) that through death He might destroy him who had the power of death, that is, the devil....
The verse clearly states that the Lord Jesus Christ was of our nature and that BECAUSE he was of our nature he was able to put to death that which has the power of death, the devil. That is to say clearly and without doubt that by means of his death the devil was destroyed. What was destroyed? the Devil.
Hebrews 9:26 ...he has appeared to put away sin by the sacrifice of Himself.
What was put away by his sacrifice? This verse clearly says that Jesus put away (destroyed) sin by the sacrifice of himself. By means of his death, sin was "put away" or destroyed.
Romans 8:3 For what the law could not do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, on account of sin (Weymouth: "as an offering for sin"): He condemned sin in the flesh...
What was condemned (put to death) by the Lord's sacrifice? Sin in the flesh.
Romans 6:3-6 Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4 We were buried therefore with him by baptism into death, so that as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life. 5 For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. 6 We know that our old self was crucified with him so that the sinful body might be destroyed, and we might no longer be enslaved to sin.
In Romans 6 our experience in the waters of baptism is a symbolic re-enactment of our Lord's death, burial, and resurrection. What do we crucify in symbol that the Lord Jesus did in reality? We crucify our "old self". Why? so that the "Sinful body might be destroyed." By means of our death to sin, by God's grace, sin is destroyed at its source, our sinful flesh, our sin-prone human nature. That's what Jesus did on the cross.
What then did Jesus put to death on the cross?
John 12:31 tells us that, by means of his being "lifted up" on the cross, the "Prince of this world" would be cast out.
Hebrews 2:14 tells us he put to death that which has the power of death, that is, the devil. However, it also tells us that, in order to do that, he had to be of the same nature as ourselves - human nature, prone to temptation and sin. He overcame his nature and put its evil propensities to death. What is it that has the power of death? Sin! That's what he destroyed, put away, cast out! (see Romans 6:23)
That's why Hebrews 9:26 says he put away (or destroyed) sin by his sacrifice. That's why Romans 6 says that the devil that was destroyed on the cross was the "sinful body" and Romans 8 tells us that "sin in the flesh" was condemned or destroyed or "cast out" by his sacrifice. The "Prince of this world" or "The Devil" is synonymous with "sin in the flesh."
Who or what is it that has the power of death? Hebrews 2 portrays it as "the devil" - in Greek, the word means a treacherous liar - Romans calls it sin in the flesh or the body of sin. Between whom is the great controversy of the ages? Is it between God and some mythical fallen angel and his minions? Not at all, it is between God and Sin in the flesh! We are the enemy of God so long as we allow ourselves to remain estranged from Him. See Romans 7 for a graphic description of this spiritual warfare but keep reading through to Romans 8:4.
Now back to Ephesians 2.
Paul says that before we came to Christ, we were dead in trespasses and sins. This is the way in which we once walked according to the "course of this world". The word "course" in Greek is aion meaning the present worldly circumstances - i.e. we lived according to the flesh like everyone else controlled by the Prince or ruler of this world.
This ruling power is the spirit of worldliness (lust of the eyes, lust of the flesh, and pride of life 1 John 2:15-7). This is the spirit that energizes all who love the world and the material things of the world. In Ephesians 2:2, what does Paul say is a synonym for "the course of this world", the "prince of this world", the "spirit working in the disobedient"? He says it is the "lusts of our flesh" and "the desires of the flesh and of the mind". We are "by nature" children of wrath.
We bear that same nature that Jesus put to death on the cross. That same nature which he calls upon us to crucify with him, by his grace and with his help as we follow him through the waters of baptism and then taking up our cross to follow him day by day until he comes to establish his Father's Kingdom and to fill the earth with his glory!
I hope you have found this helpful. If you have follow-up questions, please submit them on the thisisyourbible.com site. Thanks!