a dedicatory offering: a gift formally presented to the LORD at the sanctuary before it is handed over for sacred use
Most of the time this word names a special class of offering. The worshiper or priest takes something that still belongs to the worshiper and presents it to the LORD inside the sanctuary, marking it as set apart for God and for the priests who serve him. Older Bibles call it a "wave offering," picturing the priest swinging it back and forth, but the word covers gifts that could never be swung: bars of gold, tons of bronze, live animals, even a whole tribe of people. So the heart of the word is the act of formal presentation and dedication, not a particular hand motion. "Presentation offering" or "elevation offering" catches it better.
The three shades below are all the same basic act seen from different angles. Sometimes the word names the priest's appointed share of a fellowship sacrifice, the breast that becomes his by this rite. Sometimes it names the ceremony itself, the moment the gift is lifted up and offered before the LORD at a priest's ordination, at a cleansed person's restoration, or at the spring and early-summer festivals. And sometimes it labels large donations or consecrated people as belonging to God: the precious metal given for the tent of worship, or the Levites handed over to serve in place of Israel's firstborn.
What ties them together is the idea of transfer into the sacred sphere. A thing in ordinary hands becomes a thing that belongs to God, and this presentation is how the change is made public and official.