When Catholics say they are “going to Adoration,” they are typically referring to Eucharistic Adoration. Which, in the most basic terms, is the worship of the Eucharist outside of the Mass. The Eucharistic Host is displayed in a monstrance on the altar so that all can see and pray in the presence of Christ.
The Catechism of the Catholic Church tells us that, “Adoration is the first attitude of man acknowledging that he is a creature before his Creator. It exalts the greatness of the Lord who made us and the almighty power of the Savior who sets us free from evil. Adoration is homage of the spirit to the “King of Glory,”respectful silence in the presence of the “ever greater” God. Adoration of the thrice-holy and sovereign God of love blends with humility and gives assurance to our supplications.” (CCC 2628)
We can adore God in many ways, but in Eucharistic Adoration, we spend time adoring the true presence of Christ in the Eucharist.
Resources:
A Beginner's Guide to Adoration
A Convert's Guide to Adoration