limited atonement?

1 Timothy 4

The "L" in the "TULIP" of "Calvinism" stands for "Limited Atonement" (http://www.theopedia.com/TULIP).  I'm not sure that I understand the exact theological meaning of "Limited Atonement", but from what I have heard, the basic idea is that Jesus died only for those who believe.  But when I consider the following verses, it seems to me that Christ died for ALL:

^{John 3:16} "For God loved the world so much that he gave his one and only Son, so that everyone who believes in him will not perish but have eternal life. ¹⁷ God sent his Son into the world not to judge the world, but to save the world through him.

^{1 Tim. 4:10} This is why we work hard and continue to struggle, for our hope is in the living God, who is the Savior of all people and particularly of all believers.

^{Titus 2:11} For the grace of God has been revealed, bringing salvation to all people.

Heavenly Father, thank you for your grace and mercy through Christ.  Lord, please help me share your good news with everyone, and help me be a disciple of Christ and make disciples of Christ.  I love you, Lord, and I pray in the name of Christ.