to render the religious service a creature owes to a god: to worship, to serve God
In everyday classical Greek this word once meant plain hired labor, the work a paid servant does for wages. By the time of the New Testament that ordinary sense had fallen away completely: every one of its 21 New Testament uses is about worship, and never about secular work. The turning point was the Greek Old Testament, whose translators reserved this verb for service directed at a god (whether the true God or a false one) and used other words for ordinary servitude. So the New Testament writers inherited it as a near-technical term for the exclusive, obligated, active service that creatures owe their Creator.
The word keeps a single core meaning across all its uses, but that service shows up in several settings. Its center of gravity is the formal ritual worship of the sanctuary, the priests and their sacrifices. From there it widens: Luke and Paul use it for a whole life of devotion, prayer, and gospel ministry, and the book of Revelation uses it for the worship of the redeemed before God's throne. The same word can also be turned the wrong way, naming the worship people wrongly give to idols and created things.
What sets this word apart from its neighbors is that it names the rendered service itself, the actual doing of worship, rather than the bodily gesture of bowing (that is προσκυνέω) or the inner feeling of reverence (that is σέβομαι). It overlaps with the priestly, official service word λειτουργέω, but is broader: all official priestly service is this kind of worship, though not all of this worship is official priestly service. And unlike the plain servant word δουλεύω, which can describe secular slavery, this verb in the Bible is only ever aimed at a god.