In episode 2 of Secrets of the Cell biochemist Michael Behe explains what he means by the term irreducible complexity. Irreducible complexity is one of the key indicators of the intelligent design of life, and on classical Darwinian terms it's very difficult to explain how it could've ever evolved.
Indeed, the only serious attempt to refute Behe has been to deny that irreducible complexity actually exists in living things, but this hasn't been very persuasive.
The episode is only 5 minutes long and has some beautiful animations: