Dulia is a Greek word roughly equivalent to “service.” The word latria (or, in its ancient Greek form, latreia) is the Latin word for “worship.” In Roman Catholic teaching, latria is offered to God, but the saints receive dulia (veneration) and Mary is worthy of hyperdulia (“beyond service” or “super-veneration”).
Catholicism draws a fine line between dulia and latria, maintaining they are distinct from each other. But, in Scripture, the words worship and service are often used interchangeably or in association in reference to God or pagan gods:
The English translations speak of “worship” and “service,” while the Greek and Hebrew seem to divide worship into “fear” and “bow down before.” Even though the two or three words may have slightly different meanings, it is clear that they are all combined to be the sum total of a proper response to the Lord and an improper response to the pagan gods. Worship, service, and fear/respect are not completely separate concepts but different facets of the same response.
While the Bible seems to inseparably bind the two (or three) concepts together, the Roman Catholic Church has separated them. In Roman Catholic theology, dulia is the service or honor due to saints. Hyperdulia is the elevated service or honor due to Mary as the greatest of all saints and even more as co-redemptrix and “Mother of God.” (The prefix hyper- means “above normal.”) Latria is the worship that is due to God alone. In this way, Roman Catholic teaching can maintain that only God is worshiped, and all other acts directed toward Mary or the saints are not in violation of the command to worship God alone.
However, this seems to be splitting hairs. It is clear that, in Roman Catholic teaching and practice, faithful Catholics are instructed to respond to saints in ways that the Bible reserves for God alone. Roman Catholic teaching urges the faithful to venerate saints—again, veneration falls short of worship in their teaching. Dulia and hyperdulia are shown in doing things like visiting shrines and altars for Mary or other saints as well as praying to them for help to meet various needs, including eternal salvation.
It seems clear that dulia and hyperdulia, even as defined by the Roman Catholic Church, should be reserved for God alone.