Albert Barnes Commentary Leviticus 1:4

"And he shall lay his hand upon the head of the burnt-offering; and it shall be accepted for him to make atonement for him." — Leviticus 1:4 (ASV)

And he shall put his hand upon the head of the burnt offering—the usual ceremony. By it the sacrificer identified himself with his victim (Leviticus 3:2, 8; Leviticus 4:15; Leviticus 8:14; Romans 12:1).

To make atonement for him—this phrase belongs especially to the sin-offerings and the trespass-offerings (compare Leviticus 4:20, 26, 31, 35; Leviticus 5:16, 18; Leviticus 6:7, and so on). It is not used in reference to the peace-offerings, and only rarely in reference to the burnt-offerings. It should be noted that it is here introduced in close connection with the imposition of hands by the worshipper, and not—as it is when it refers to the sin-offering—with the special functions of the priest (Leviticus 4:26, 35; 2 Chronicles 29:23).