This is a good read from gotquestions.org. The link is http://www.gotquestions.org/predestination.html.
I am pasting the content from the link above for easy consumption and understanding. All rights and authorities are with gotoquestions.org
"What is predestination? Is predestination biblical?"
Answer: Romans 8:29-30 tells us, “For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers. And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.” Ephesians 1:5 and 11 declare, “He predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will…In him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will.” Many people have a strong hostility to the doctrine of predestination. However, predestination is a biblical doctrine. The key is understanding what predestination means, biblically.
The words translated “predestined” in the Scriptures referenced above are from the Greek word proorizo, which carries the meaning of “determine beforehand,” “ordain,” “to decide upon ahead of time.” So, predestination is God determining certain things to occur ahead of time. What did God determine ahead of time? According to Romans 8:29-30, God predetermined that certain individuals would be conformed to the likeness of His Son, be called, justified, and glorified. Essentially, God predetermines that certain individuals will be saved. Numerous scriptures refer to believers in Christ being chosen (Matthew 24:22, 31; Mark 13:20, 27;Romans 8:33, 9:11, 11:5-7, 28; Ephesians 1:11; Colossians 3:12; 1 Thessalonians 1:4; 1 Timothy 5:21; 2 Timothy 2:10; Titus 1:1; 1 Peter 1:1-2, 2:9; 2 Peter 1:10). Predestination is the biblical doctrine that God in His sovereignty chooses certain individuals to be saved.
The most common objection to the doctrine of predestination is that it is unfair. Why would God choose certain individuals and not others? The important thing to remember is that no one deserves to be saved. We have all sinned (Romans 3:23), and are all worthy of eternal punishment (Romans 6:23). As a result, God would be perfectly just in allowing all of us to spend eternity in hell. However, God chooses to save some of us. He is not being unfair to those who are not chosen, because they are receiving what they deserve. God’s choosing to be gracious to some is not unfair to the others. No one deserves anything from God; therefore, no one can object if he does not receive anything from God. An illustration would be a man randomly handing out money to five people in a crowd of twenty. Would the fifteen people who did not receive money be upset? Probably so. Do they have a right to be upset? No, they do not. Why? Because the man did not owe anyone money. He simply decided to be gracious to some.
If God is choosing who is saved, doesn’t that undermine our free will to choose and believe in Christ? The Bible says that we have the choice—all who believe in Jesus Christ will be saved (John 3:16; Romans 10:9-10). The Bible never describes God rejecting anyone who believes in Him or turning away anyone who is seeking Him (Deuteronomy 4:29). Somehow, in the mystery of God, predestination works hand-in-hand with a person being drawn by God (John 6:44) and believing unto salvation (Romans 1:16). God predestines who will be saved, and we must choose Christ in order to be saved. Both facts are equally true. Romans 11:33 proclaims, “Oh, the depth of the riches of the wisdom and knowledge of God! How unsearchable his judgments, and his paths beyond tracing out!”