A quick search on the web led to quite a few articles on the subject.
Here is one that defends the doctrine:
http://www.the-highway.com/articleAug02.html
The same search of the web gave a few, though not nearly as many, articles against the doctrine. But all of the arguments against it can be refuted by the arguments for it.
Basically, predestination is the teaching that God has determined before hand what will happen in order to accomplish His will. The concept is tied together with God's foreknowledge of all things that will ever happen. It admittedly is a tough topic to explain, but AA Hodge's article above is pretty well put together. Are there any specific questions you have with regards to the subject? Without any specific questions, it's hard to really give a catch-all answer without linking to big articles like this that goes over the entire thing.