I am the good shepherd; I know my sheep and my sheep know me--just as the Father knows me and I know the Father--and I lay down my life for the sheep.
Definite redemption, sometimes called "particular redemption," "effective atonement," and "limited atonement," is an historic Reformed doctrine about the intention of the triune God in the death of Jesus Christ. Without doubting the infinite worth of Christ's sacrifice or the genuineness of God's "whoever will" invitation to all who hear the gospel (Rev. 22:17), the doctrine states that the death of Christ actually put away the sins of all God's elect and ensured that they would be brought to faith through regeneration and kept in faith for glory, and that this is what it was intended to achieve. From this definiteness and effectiveness follows its limitedness: Christ did not die in this efficacious sense for everyone. The proof of that, as Scripture and experience unite to teach us, is that not all are saved.
The only possible alternatives are (a) actual universalism, holding that Christ's death guaranteed salvation for every member of the human race, past, present, and future, or (b) hypothetical universalism, holding that Christ's death made salvation possible for everyone but actual only for those who add to it a response of faith and repentance that was not secured by it. The choices are, therefore, an atonement of unlimited efficacy but limited extent (Reformed particularism), one of unlimited extent but limited efficacy (hypothetical universalism), or one of unlimited efficacy and unlimited extent (actual universalism). Scripture must be the guide in choosing between these possibilities.
Scripture speaks of God as having chosen for salvation a great number of our fallen race and having sent Christ into the world to save them (JOHN 6:37-40, 10:27-29, 11:51-52; Rom. 8:28-39; Eph. 1:3-14; 1 Pet. 1:20). Christ is regularly said to have died for particular groups or persons, with the clear implication that his death secured their salvation (JOHN 10:15-18,27-29; Rom. 5:8-10, 8:32; Gal. 2:20, 3:13-14, 4:4-5; 1 John 4:9-10; Rev. 1:4-6, 5:9-10). Facing his passion, he prayed only for those the Father had given him, not for the "world" (i.e., the rest of mankind, JOHN 17:9,20). Is it conceivable that he would decline to pray for any whom he intended to die for? Definite redemption is the only one of the three views that harmonizes with this data.
There is no inconsistency or incoherence in the teaching of the New Testament about, on the one hand, the offer of Christ in the gospel, which Christians are told to make known everywhere, and, on the other hand, the fact that Christ achieved a totally efficacious redemption for God's elect on the cross. It is a certain truth that all who come to Christ in faith will find mercy (JOHN 6:35,47-51,54-57; Rom. 1:16, 10:8-13). The elect hear Christ's offer, and through hearing it are effectually called by the Holy Spirit. Both the invitation and the effectual calling flow from Christ's sin-bearing death. Those who reject the offer of Christ do so of their own free will (i.e., because they choose to, Matt. 22:1-7; JOHN 3:18), so that their final perishing is their own fault. Those who receive Christ learn to thank him for the cross as the centerpiece of God's plan of sovereign saving grace.
From: Concise Theology: A Guide To Historic Christian Beliefs