When the rebellous angels were thrown out of Heaven, their disobedience to God created Hell, the spiritual state of separation from God. The Lord did not yet send the devils to Hell, but He when He promised man a Redeemer in Genesis 3:15, He basically told the devils, “I’m going to heal the world of all the damage you have caused, and though you will try to stop Me, I will triumph over you and you will rightfully go to Hell for having rejected Me in spite of your great knowledge of Me.” (An angel’s knowledge of God far exceeds the wisdom of man).
The demons knew God was speaking the truth, yet in spite of this knowledge they did exactly what He had said: they led many men away, they attacked Israel, they did everything they could to frustrate God’s plans. But in their work, they unwillingly aided God in His plans, for He always brought a greater good out of evil. Even when they led Jesus to death, thinking they were literally killing God - and so accomplishing what they had always wanted, so as to stop God from sending them to Hell and so as to make His creatures and creations suffer out of hatred for God - they unwillingly aided the Lord, for by His Holy Sacrifice the Lamb redeemed the world.
Whenever Jesus exorcised a devil, it would always cry out, “Have you come to torment us before the appointed time?!” The appointed time was the messanic age, the time when the Messiah would heal the world of all evil - including the possession of individuals by devils. The demons feared the coming of the Messiah because they knew He would send them to Hell. And this why devils hate exoricsm.
When a priest exorcises a demon, the evil spirit goes to Hell. This is why demons will sometimes ask priests to send them into animals or to deserts, because they wish to stall their torment. Once a devil goes to Hell, it can never leave Hell, and becuase it can never leave Hell, it can never harm anyone or anything ever again. Once a demon goes to Hell, it loses its power over man. Spirits are power itself - they are beings who are made of will, intellect, and imagination, and hence, they are made of power - so when a spirit loses its power, it spiritually dies: it dose not actually die, since it is immortal, but it can’t do anything at all ever again, it is completely helpless, pathetic, and has no reason left to exist. This why demons despise priests and accuse them all of being murderers.
Whenever a Christian makes the Sign, any demons in the room flee at once. They cannot withstand the Sign of the Cross, because it is the power of Jesus - literally. Christians share in the priestly office of Jesus, and just as He gave His Apostles the power to drive out devils, so too, all Christians share in this healing power, though the laity share in it in a lesser decree than the priests. Every Christian is able to perform minor excorisms - prayers, such as the Sign and the Prayer to Saint Michael - but only the priests are able to perform major exorcisms - the rite of exorcism, whereby a possessed man is freed from the devil’s power - becuase the priests act in the Person of Christ. The Sign of the Cross is the power of God over the demons: the devils cannot overcome God, they do not have such power to withstand Him, they are not that great, and the Death of Jesus proved this, and so, they flee whenever a Christian signs himself.
This is one of the reasons why Christians are encouraged to cross themselves whenever they eat and sleep, work and rest, get up and sit down, go here and there, do this or that. They exorcise the world, they heal the world, by prayer.