When John the Baptist first laid his eyes upon Jesus he said, “Behold, the Lamb of God, who takes away the sin of the world!” (John 1:29, ESV) Here John the Baptist is giving his view of the atonement. Jesus would be the sacrificial/passover lamb, that spills His blood, to cover the sins of the world. Jesus' life, death, and resurrection are paying a ransom or redemption price that will take away the sin of the world. As the Israelites found shelter under the blood of the passover lamb, and the wrath of God passed over them, so will the world find shelter from the wrath of God under the blood of Christ.
The question is, who is the world? Some would be quick to say, it is everyone all over the earth. If that is true, then Jesus' death has been counted to all men and everyone’s sins have been forgiven. This is the heresy of universalism and not true as Jesus says in John 3:36, “Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him.”
Others would argue that Jesus death covers some of the sins of all men, but they must believe in Jesus death and resurrection to have all of their sins forgiven. This is illogical, isn’t a person’s unbelief also a sin? Did Jesus not die for that sin as well as all others? If this was the case, Jesus’ death could have been for naught. It would have been a theoretical possibility that Jesus’ death actually saved no one, it simply made salvation possible for some. What actually saved a person was them placing their faith in Jesus. So Jesus could have died and been resurrected only for the whole world to reject Him and that would have accomplished nothing and would not have “taken away” the sin of anyone.
Then just what did John the Baptist mean by “the world?” I contend, that John the Baptist meant that Jesus died for all the sins of some men from all around the World. Namely, Jesus died for all of his elect who are from every tribe, nation, language, age, gender, ethnicity, etc. Jesus' death and resurrection made certain the salvation of all of God’s people. This view of the extent of the atonement is called Particular Atonement.
In the 17th Century, John Owen broke it down like this:
The Father imposed His wrath due unto, and the Son underwent punishment for, either:
I ask, Is this unbelief a sin, or is it not? If it be, then Christ suffered the punishment due unto it, or He did not. If He did, why must that hinder them more than their other sins for which He died? If He did not, He did not die for all their sins!"