Concise Bible Dictionary:

This principally refers to the consecration of Aaron and his sons to the priestly office, which is given in detail in Exodus 29 and Leviticus 8. They were washed, clothed, and anointed with oil. One bullock was offered for a sin offering, and one ram for a burnt offering; another ram was offered, and this ram is called “the ram of consecration:” its blood was put upon the right ear, the thumb of the right hand, and the great toe of the right foot. Aaron and his sons were sprinkled with blood and anointed with oil. Parts of the ram were placed in the hands of Aaron and his sons, these were waved before the Lord, and then burnt on the altar upon the burnt offering. The breast of the ram was also waved before the Lord and was for Moses. Aaron and his sons ate of the flesh and other consecrations at the door of the Tabernacle.
The words mostly used for “to consecrate” are mala yad, which signify “to fill the hand” (as often rendered in the margin), doubtless alluding to their taking portions of the ram into their hands and waving them before Jehovah. Their hands being filled with offerings was suited to their character as priests to God. All was typical of believers being cleansed by water, sprinkled with blood, and anointed with oil: entirely consecrated to God, and constituted a priestly company for worship in the holiest.

From Anstey’s Doctrinal Definitions:

This term is from the Old Testament, but the truth of it is also found in the New Testament, even though the word isn’t. Consecration means, “to fill the hands” (Ex. 32:2929For Moses had said, Consecrate yourselves to day to the Lord, even every man upon his son, and upon his brother; that he may bestow upon you a blessing this day. (Exodus 32:29) – margin; 1 Kings 13:3333After this thing Jeroboam returned not from his evil way, but made again of the lowest of the people priests of the high places: whosoever would, he consecrated him, and he became one of the priests of the high places. (1 Kings 13:33) – margin). A “consecrated” Christian is one who has his hands full in the discharge of his service for the Lord. He is busy in the things of the Lord, and this to the point where he doesn’t have room for extraneous things in his life.
This is illustrated in the consecration of the priests in the Old Testament. In Exodus 29, after Aaron’s sons were washed with “water” (vs. 4), sprinkled with blood (vs. 20), and anointed with oil (vs. 21), Moses filled their hands with ten things that typify Christ in various ways (vss. 22-24). If we could picture those priests in our minds standing there on that day with all those things in their hands, we would immediately understand that they didn’t have room for other things. Similarly, a consecrated Christian is a focused individual whose life is full with the service of the Lord.
Oftentimes dedication is confused with consecration, but there is a difference: