Here's Webster's 1828 definition (http://www.cbtministries.org/resources/webster1828.htm):
PREDESTINA'TION, n. The act of decreeing or foreordaining events; the decree of God by which he hath, from eternity, unchangeably appointed or determined whatever comes to pass. It is used particularly in theology to denote the preordination of men to everlasting happiness or misery.
Predestination is a part of the unchangeable plan of the divine government; or in other words, the unchangeable purpose of an unchangeable God.
Let's look at the word "foreknow."† The Greek word is "Proginosk".
From crosswalk.com's interlinear (http://www.biblestudytools.net/Lexicons/Greek/grk.cgi?number=4267&version=kjv):
1. to have knowledge before hand
2. to foreknow
††† a. of those whom God elected to salvation
3. to predestinate
This same Greek word is used in 1 Pet 1:20 as "foreordain":† "Who [Christ] verily was foreordained before the foundation of the world, but was manifest in these last times for you,"
So, we can see that foreknowing is tied with foreordaining:† God knows something before hand because He has ordained it to happen before hand.† God foreknows His chosen because He foreordained them to be as such.
Along with that, knowing someone does not necessarily mean just a cognitive recognizing of someone.† There are many examples in the Bible where someone was known, but it didn't mean cognitively, it meant intimately:† Adam knew his wife (Gen 4:1); Mary not knowing Joseph (Luke 1:34); the Pharisees not knowing the Father (John 8:19).
And here's the kicker:† those people standing before the Lord who did works in His name He says He NEVER knew (Matt 7:22-23).† NEVER knew?† Can't be cognitive only; must be a different kind of knowing.† He never had an intimate knowledge of them, because He never ordained it to be as such.
Now, let's look at man.† At the fall, man lost the spiritual ability to seek after God.† Rom 3:11 - "There is none that understandeth, there is none that seeketh after God."† NONE seek after God.† Also, John 6:44 - "No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day."† NO MAN CAN come to Jesus, except the Father draw him.† The word "draw" in the Greek paints a picture of water being drawn out of a well.† Also, there is Jesus raising Lazarus from the dead, where during that scene Jesus talks about He being the resurrection and the life, and though one is dead, yet shall he live (John 11).† We were DEAD in our sins (Eph 2:1,5; Col 2:13).† It is impossible for us to come to God on our own.
So, how can we?† A person is quickened and given a heart of flesh, replacing the heart of stone, causing us to walk in His statutes (Eze 36:26-27).† A person is given the gifts of faith, belief and repentance (Eph 2:8: Phil 1:29; 2 Tim 2:24-25, to name a few); and it is according to His grace and His will that all of these things be done (many verses about election, John 1:12-13 and Rom 9 being some).
Which leads to the election topic, with which the Bible is replete of verses regarding that topic.
So, put it all together, and we have the picture of God ordaining and choosing, man incapable, and God effectively making it happen.
One final thought:† if God's predestining of people is based on Him knowing that we would choose Him at some point, why does He need to predestinate anyone knowing that with or without His predestining, they would choose Him?