Mystically Speaking: (-Leviticus 1:2), “When a man brings (יַקְר ִ֥יב - from the etymology: ‘near’) --he must bring the offering:-- from you an offering (קָרְ בָָּ֖ן מ כ ֶּ֛ם) to the L-rd.” All other mitzvot are “limbs” and “sinews (248 Positive Commandments: 248 organs (of a male’s organs, not including the reproductive organs of the female). 365 Prohibitions: 365 Sinews of the human body), each mitzvah being a different organ or sinew of ours that we are bringing near to, and giving to G-d.
However, a sacrifice is about one giving themselves over, bringing themselves near, entirely to G-d. --This is emphasized in the teaching of Nachmanides (-Leviticus 1:9) as to why offerings bring atonement, “A person should realize that he has sinned against his G-d with his body and his soul, and that his blood should really be spilled and his body burned, were it not for the loving-kindness of the Creator, Who took from him a substitute and a ransom, namely this offering, so that its blood should be in place of his blood, its life in place of his life, and that the chief limbs of the offering should be in place of the chief parts of his body.”
More so, the concept of offerings are in their context that of teshuvah (Repentance). Teshuvah is above all mitzvot, and thus, in can fill any blemish created through sin and negation of a mitzvah.
