Teleology is a philosophical principle strongly related with Christianity (and other determinist religions) that states that everything in the universe is moving towards some final end. Whereas typical science seeks to attribute cause to explain effects, teleology would instead accept the cause, whatever it may be, as simply that which was necessary to elicit the effect. Teleology is more concerned with the effect, and how it serves to further the inevitable progression towards that ultimate end. Teleology does not refute science, but rather embraces it in an awkward way, claiming that when sufficient causality is assigned in the form of scientific laws, this will inevitably demonstrate some directive principle that guides everything.
One field in which theologians have applied teleology is evolution. At the most basic level, there are two parts to evolution: random chance, which determines mutations and things of that ilk, and natural selection, which tends to determine which variations survive and procreate. Teleology would claim that the random chance aspect is not truly random, but instead acts upon the directive principle to determine what mutations occur. Likewise, natural selection can be influenced by other factors, such as natural disasters, which would skew the statistically anticipated survival rates. Teleology would also attribute these factors to their directive principle. The Catholic Encyclopedia summarizes this by asking whether "man sees because he has eyes or has eyes in order to see".
Thomas Aquinas wrote of teleology, "As the influx of the efficient cause consists in its own action, so the influx of the final cause consists in its being sought after and desired." By this, he meant that the directive principle was the sum total effort of men to better themselves. Though this is fraught with circular logic so typical of Aquinas (the objective exists because of the ideal, and the ideal exists because of the objective), it summarizes rather concisely the thoughts and mindset of many who buy into the idea of teleology.
The main issue on which supporters of teleology differ is whether the pursuit of the end is intentional or if it is instead an inherent, unconscious will. Those who claim the former tend to believe that the ultimate end will be achieved when everyone acts for the will of God. Supporters of the latter tend to claim that everything that happens is a piece of God's master plan, and when that plan comes to fruition, the ultimate end will be achieved.
Sources:
http://www.newadvent.org/cathen/14474a.htm
http://ase.tufts.edu/cogstud/papers/evoltele.htm
http://pespmc1.vub.ac.be/ASC/TELEOLOGY.html