From Desiring God blog:
Here’s a conversation between an unbeliever and an evangelist who believes in the doctrine of [Substitutionaary or Actual Atonement] definite atonement (sometimes unhelpfully called “limited atonement”)—the biblical teaching that when Jesus died, God’s unalterable purpose was to cancel the sins and commute the death sentence of all whom he would give to the Son (John 6:39).
Unbeliever: So what are you offering me?
Evangelist: Salvation from God’s wrath and from your sin. Everlasting life.
E: Because when Jesus, the Son of God, died, he absorbed God’s wrath, removed it, and he bore the guilt of sin for all who trust him.
U: Did he do that for me?
E: If you will have him—receive him—you will have all that he is for you and all that he did for you. If you will trust him, yes, he did it for you.
U: So you don’t know if he did it for me?
E: He is offering himself to you right now freely. He is offering you a wonderful, finished work of redemption—all that he accomplished in absorbing God’s wrath and cancelling sins. All of that is yours for the having, right now. If you won’t have it, it’s not yours. If you will, it is. There’s only one way to know if your sins were cancelled and your death sentence was commuted in the death of Jesus. Believe on him. His promise is absolute: If you believe, you will be saved. If you won’t believe, you remain in your sin, and under God’s wrath.
U: So what are you asking me to receive?
E: Jesus. Receive Jesus! Because Jesus really did these things. He really secured the freedom of his people from the wrath of God. He really bore their sins in his body on the tree. If you receive him, you are one of them. You are included. All that is true for you. He offers to you freely right now.
U: I thought I could know Jesus died for me before I believed? That’s what I’ve always been told: Believe on him, because he died for everybody.
E: I can’t say for sure, but the people who taught you that probably meant this: Jesus died so that the gospel could be offered to all, and all who believe would be saved. That’s true. But if I assured you before you believe that your sins were cancelled and your freedom from God’s wrath was obtained, I would mislead you. Imagine if I said to you, Jesus certainly obtained your deliverance from God’s wrath and certainly covered all your sins. Now believe that. What would you say?
U: I’d say, great. Now what if I don’t believe? Then I’m still saved, right? Since my sins were certainly covered. It’s done.
E: Yes, that’s probably what you would say, and you’d be wrong. Because I would have misled you. The good news that Jesus has for you before you believe on him is not that your sins are certainly cancelled. The good news is that Jesus really propitiated the wrath of God, and really covered the sins of his people. It is finished. And that is what I offer you. It’s free. It’s full. It’s complete. It’s glorious. And his absolute promise to you is this: It’s yours if you will receive him. Believe on the Lord Jesus Christ, and you will be saved.