Deliverance is any prayer to God, the angels, or the saints asking to be freed from the power of the Evil One and the kingdom of darkness. Technically, we pray deliverance every single time we say the Our Father. The authority to pray deliverance is derived directly from one’s Baptism. It cannot be taken away. If you have been baptized “in the name of the Father, and the Son, and the Holy Spirit,” you possess a general authority against demons (although you should never undertake this kind of action without considerable training and a direct calling from God).
Deliverance is also a term which is used to describe specific ministries or prayer sessions which are conducted with intent to expel demons. While ordinary demonic activity, such as everyday temptation, are largely defended against by living the good Catholic life, there are special cases where the kingdom of darkness has managed to gain a legal right to act above and beyond mere temptation in a person's life. This is called extraordinary activity. In most cases, the primary means of casting out (or removing) from someone’s life this insidious activity of the Devil comes through two special forms of prayer: minor (or simple) exorcisms and major (or solemn) exorcisms.
In this case, deliverance is a series of private minor exorcism prayers. They are permitted to the laity and normally performed by a trained deliverance counselor over those who suffer from some form of extraordinary demonic activity. After the victim of such demonic activity has willingly participated in the Sacrament of Reconciliation with a Catholic priest, these kinds of prayers are said over the afflicted person by a deliverance counselor (or even by the afflicted person himself, if he knows how to do it) in order to break the bonds that any evil spirits may have over him. This act brings about a greater freedom for the person than if the prayers had not been said.
In fact, if you think about the process that adults undergo to become Catholic through RCIA (the Rite of Christian Initiation for Adults), you see a parallel structure that exists between deliverance and initiation into Christianity. First, the candidate goes to Confession. Then, when he is at the Easter Vigil, he is Baptized, he renounces the Devil publicly, and then he is prayed over by the priest in the form of a minor exorcism. So the legal rights of the Devil over the initiated person are broken when he confesses his sins to God and is forgiven, then he renounces the Devil verbally, and the priest casts the Devil out with a prayer of deliverance.
This is basically the same step-by-step process we follow in our model of deliverance.
It's also important to note that this is why it is so critical that we, as Christians, attend Confession regularly and pray the acts of penance assigned to us by the priest. The Sacrament breaks any hold the Devil might have over us after we have willingly chosen to sin, and when we perform the assigned acts of penance, which usually include the Our Father or the Hail Mary, these prayers drive out the demons attached to us as a result of our sin.
According to Fr. Fortea, an exorcist in Madrid, who spoke on the subject of deliverance prayers and the Rite of Exorcism: “God, in His wisdom, has not desired to place too many conditions on the most essential Christian practices for them to be valid (e.g., baptism or exorcism).” In other words, Christians of all kinds technically have this authority over demons because of the primary reason the Kingdom of God was inaugurated by Christ: to expel demons from our lives, freeing us from sin and demonic bondage, so that we can know and accept Jesus Christ as our Lord and Savior and become baptized and enter His Church.
In fact, in many cases, Catholic exorcists rely on deliverance counselors or similar prayer groups to alleviate their heavy caseloads. This is because an exorcist is first a priest: he must still perform all the duties required of him by his office. The exorcist appointment is a secondary function, so you can see that, as busy as priests are, they cannot always handle every minor case that comes their way. The Devil often tries to wear the exorcist down through such busyness, so when a particular case is not as severe as full possession, it is often a blessing for the exorcist to direct the client towards a local deliverance counselor, who can handle the less severe cases of demonic activity.
But it is important now for me to draw your attention to something very important about exorcism in general: even the Rite of Exorcism, which is the highest form of exorcism prayer that is available within the Church, is merely a sacramental. The Rite is not a full Sacrament. This is very important to understand. All prayers of deliverance, from the Rite itself to those deliverance prayers permitted to the laity, exist upon the firm foundation laid by two critically important Sacraments: Baptism and Reconciliation. Exorcism prayers would not be possible otherwise. This is because a layman's authority to cast out or rebuke demons, which was handed down to him directly by Jesus Christ, exists by virtue of the individual's Baptism. However, even when a Christian has the authority to use an exorcism prayer such as this, the Devil's legal right to the afflicted person must be broken first. And how is this done? Through the Sacrament of Reconciliation. In most cases, when the Devil has an extraordinary influence in a person's life, it is because of the person’s own free will choices, their own sin, in other words. So, the person must first confess these sins (i.e., participate willingly in the Sacrament of Reconciliation) before he--or a person with spiritual authority over him--can exercise the Christian authority to cast out a demon (i.e., by virtue of the Christian's Baptism).
In conclusion, the Sacraments of Baptism and Reconciliation are twin pillars which hold aloft prayers of deliverance and make it possible for the Christian to use them against the demonic kingdom. This is why it is necessary to first become a baptized Christian in order to find freedom from bondage, and why it is necessary for an already baptized Christian who is under the influence of diabolic activity to confess their sins regularly, with haste. As you can see, while deliverance is an important ministry, and it certainly has its place within the Church, in the end, it is the Sacraments which truly free us!