Israel was under Mosaic Law, of course, and the New Testament Covenant has freed us from the obligations of those liturgical instructions. However, they were a "schoolmaster" (Galatians 3:24) to teach us about the relationship of God to His people.
This voluntary offering was designed to be given at various times and for many reasons—but if offered in "Thanksgiving" it was to be specially performed, as explained below.
The drama tells the story of Thanksgiving to God.
"By placing his hand upon the head of the animal, which had been brought to the altar of Jehovah for the purpose, the offerer signified that with this gift, which served to nourish and strengthen his own life, he gave up the substance of his life to the Lord, that he might thereby be strengthened both body and soul for a holy walk and conversation. To this end he slaughtered the victim and had the blood sprinkled by the priest against the altar, and the fat portions burned upon it, that in these altar-gifts his soul and his inner man might be grounded afresh in the gracious fellowship of the Lord. He then handed over the breast-piece by the process of waving, also the right leg, and a sacrificial cake of each kind, as a heave-offering from the whole to the Lord, who transferred these portions to the priests as His servants, that they might take part as His representatives in the sacrificial meal." (Biblical Commentary on the Old Testament; The Pentateuch, vol. II; Keil & Delitzsch, Eerdmans, Grand Rapids, p. 330.)
Our "offerings" should be as honestly committed.
Think of the obvious comparisons: that which is used to "nourish and strengthen" our lives is offered in "thanksgiving" on the Lord's altar—to the Lord—which the Lord then gives a portion back as subsistence to those who serve Him. These voluntary "offerings" are freely given in thanksgiving to others who serve the Lord.
