What is Eucharistic Adoration?
Since it is the Eucharist which, at Mass, has become, by the Holy Spirit, the true Body and Blood, Soul and Divinity of Jesus Christ, no longer bread and wine although under the appearance of bread and wine, and since it is through the Eucharist that we are nourished and established as members of His Body to become His Body, it is fitting that we should have the opportunity to come and be with Him in his Eucharistic Presence outside of Mass whenever necessary or desired. During this time we can be strengthened and consoled as we give Christ our thoughts, concerns, and praises. Adoration can be done at any time when Jesus is present in the tabernacle, but during this unique time of Adoration, He is exposed, albeit under the appearance of bread and wine, so that we may see Him as our nourishment, our strength, and our sustenance of life.
Why is exposition in the monstrance preferred?
To see Jesus visibly present under the appearance of the small white host is much more conducive to intimacy than hidden away in the tabernacle. Moreover, it adds an extra responsibility on the adorers to be sure to be faithful to the hours they are scheduled, since the suggested norm for having Jesus exposed in the monstrance is that there should be at least two adorers present, and He must never be left alone. Could not these words of our Lord be applied today: "Indeed, this is the will of My heavenly Father, that everyone who looks upon the Son, and believes in Him, shall have eternal life. Him I will raise up on the last day."
Summary of Doctrine on the Eucharist
The greatest of the seven sacraments is the Holy Eucharist. The Catholic Church teaches that in the Eucharist, Our Lord Jesus Christ, true God and true man, is really present under the appearances of bread and wine. Our Lord is not merely symbolized by the bread and wine; nor is he present only through the faith of those present. Rather, the two material things, bread and wine, are completely changed into the body and blood of Jesus Christ, leaving behind only their sensible appearances. Thus, through the words of consecration spoken by the priest, Jesus, without ceasing to be present in a natural way in heaven, is also present sacramentally, body, blood, soul and divinity, in many places throughout the world.
The Eucharist is not only a sacrament but also a sacrifice. In it Jesus, acting through the priest, makes present again in an unbloody manner the sacrifice which he offered once for all by shedding his blood on Calvary. In Holy Communion, by obeying Jesus' command to eat his flesh and drink his blood, the faithful are also united spiritually with Jesus himself, and they unite their own prayers, works and sufferings to his perfect sacrifice.
Links on Eucharistic Adoration
From the Summa Theologica (St. Thomas Aquinas):
General Eucharistic Information: