Put simply, Christ died only to save the elect, securing with absolute certainty their salvation. This is not to teach that there is anything lacking in the power of God, perhaps suggesting that he is not able to save all men. Rather, God's Word indicates that it was the Father's intention that his Son was to suffer and die only for his chosen people, atoning for their sins alone. Christ's atonement was limited only in extent, not in power, according to the sovereign will of God.
In the Bible we read that the Lord's servant (Jesus) would see the results of his work (his atoning sacrifice) and "be satisfied" (Isaiah 53:11). But also, Jesus stated plainly that there are many who are heading for eternal destruction (Matthew 7:13). We can only reconcile these two statements if we understand that Christ died only for a limited number of people - for God's elect.
Scripture references: Acts 20:28; John 3:14+15; Galatians 1:4+5; Revelation 13:8; John 6:38+39; John 17:9,10+24; John 10:11; 1 Peter 2:21; Romans 5:8-10; 1 Thessalonians 1:10; Romans 8:33+34; Luke 1:68; Revelation 5:9; Isaiah 53:11.
8But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
9Since we have now been justified by his blood, how much more shall we be saved from God's wrath through him! 10For if, when we were God's enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life!Romans 8:33-34
33Who will bring any charge against those whom God has chosen? It is God who justifies. 34Who is he that condemns? Christ Jesus, who died—more than that, who was raised to life—is at the right hand of God and is also interceding for us.