Limited atonement is the doctrine that teaches Jesus did not die for all. Instead, with his perfectly obedient life and sacrifice, He completely satisfied the justice of the Father and therefore purchased salvation (ever lasting life & reconciliation) for those the Father gave Him. These people are known in the Bible as the elect.
I believe that Christ came to complete Redemption. He did not come to open the door, or make salvation possible. Jesus did his job and he did all the way. He came to buy with his blood the souls of the elect. And that’s what his life, death and Resurrection accomplished. Anything less than this belief is unBiblical (in my opinion). How can a just, righteous God punish men twice for their sins? If Christ did in fact atone for the sins of all how could a just God then send one person to Hell? We go to Hell because of sin. Believers are going to heaven because Christ atoned for their sins. If Christ atoned for the sins of all, then Hell would not exist. Yet, the Bible is clear it does. So, if you reject limited atonement you are left with universal salvation or works based salvation, both of which are not Biblical in the least.
But what does Scripture say?
21She will bear a son, and you shall call his name Jesus, for he will save his people from their sins.” -Mat. 1:21 (emphasis mine)
12he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption.-Heb. 9:12 (emphasis mine)
37All that the Father gives me will come to me, and whoever comes to me I will never cast out. 38For I have come down from heaven, not to do my own will but the will of him who sent me. -John 6:37,38
24So the Jews gathered around him and said to him, “How long will you keep us in suspense? If you are the Christ, tell us plainly.” Jesus answered them, “I told you, and you do not believe. The works that I do in my Father’s name bear witness about me, 26but you do not believe because you are not part of my flock. 27 My sheep hear my voice, and I know them, and they follow me. 28 I give them eternal life, and they will never perish, and no one will snatch them out of my hand. 29My Father, who has given them to me,is greater than all, and no one is able to snatch them out of the Father’s hand. -John 10:24-19 (emphasis mine)
For further reading I suggest:
The book of Romans (this book so clearly laid out all the doctrines of grace/TULIP for me)
The Atonement: Limited Or Unlimited? (Note: This is a 31 pg pdf file)
Tom Ascol: On Why Every Christian Must Believe Limited Atonement