I'll preface my response with I'm no theologian - heck I'm not even a very good Christian - but here is what I understand of unconditional election.
It can be a hard thing to wrap your brain around at first - but if God is omnipotent and truly God then there is nothing that happens in time that he has not already pre-ordained or planned. Nothing occurs that is random or by chance. If you believe that - then you believe in a God that also has limitations. The God of the Bible is God over all and is limited by nothing.
Where unconditional election falls into this - is that God knew before the creation of the world who would be saved and who wouldn't be. This knowledge is not based on the foreknown actions of people however - it is based on His plan and purposes and whom He chose to be saved. This all hinges upon the fact that God is God and he as creator has put everything into motion per His perrogative and His design.
This is not something we should get hung up on as human beings however - it simply is by God's very sovereign nature that he has chosen some to be saved and others not. He is the one who knows - and not us - and I quite frankly think it is something that we should not get hung up on when contemplating salvation. It IS something we should get hung up on when contemplating his soveriegnty however.
The bottom line is that we don't know who is elected and who isn't - and the purpose of this doctrine is not for us to run around trying to figure out who is and isn't. As Christians we are to preach the gospel to all - and I think we should do so with the belief that whoever we preach to we should do so with the hope that they will accept the truth and be saved.
I would be remiss if I didn't drop some verses that support the doctrine of election however. Here are two:
"For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will--to the praise of his glorious grace, which he has freely given us in the One he loves." (Eph 1:4-6).
"And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified." (Rom 8:30).
You can read far more about it by more qualified folks than me here:
http://www.monergism.com/directory/link_category/Doctrines-of-Grace/Unconditional-Election/