Think of it like how a father would push his son out of the way of a moving car (with him giving his own life) so as to save his son. It's giving your life for another. This is essentially the concept behind the: "Substitutionary Atonement." For do you not believe Jesus died for our sins?
Anyways, I see the Substitutionary Atonement in the following verses.
"Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed." (1 Peter 2:24).
4 "Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
5 But he
was wounded for our transgressions,
he was bruised for our iniquities: the chastisement of our peace
was upon him; and with his stripes we are healed."
(Isaiah 53:4-5).
"...For even Christ our passover is sacrificed for us" (1 Corinthians 5:7).
"The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world." (John 1:29).
"For even the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many." (Mark 10:45).
"I am the good shepherd: the good shepherd giveth his life for the sheep." (John 10:11).
"For he hath made him
to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5:21).
"...that he by the grace of God should taste death for every man." (Hebrews 2:9).
"Who was delivered for our offences, and was raised again for our justification." (Romans 4:25).
"Greater love hath no man than this, that a man lay down his life for his friends." (John 15:13).
"And Abraham lifted up his eyes, and looked, and behold behind
him a ram caught in a thicket by his horns: and Abraham went and took the ram, and offered him up for a burnt offering in the stead of his son." (Genesis 22:13).
21 "And Aaron shall lay both his hands upon the head of the live goat, and confess over him all the iniquities of the children of Israel, and all their transgressions in all their sins, putting them upon the head of the goat, and shall send
him away by the hand of a fit man into the wilderness:
22 And the goat shall bear upon him all their iniquities unto a land not inhabited: and he shall let go the goat in the wilderness."
(Leviticus 16:21-22).
Oh, and here is a beautiful animated music video that alludes to the Substitutionary Atonement.
I hope you like it.
May God bless you.