The answer is a bit muddled, because it seems that every major proponent has his own flavor of ID. Michael Behe, one of the most famous, posits that “irreducible complexity” is the key to detecting intelligent design. An irreducibly complex system is one in which if you remove any of the component parts, the whole thing stops working. As such, it could not possibly have evolved through natural selection since those multiple, interconnected parts would all have to have arisen simultaneously. This ignores such concepts as I alluded to earlier: mosaic evolution and exaptation. It also capitalizes on our present lack of knowledge regarding the evolutionary history of many complex systems: if we can’t explain how it evolved via natural selection, then the reason must lie in the fact that it didn’t evolve via natural selection, and was therefore designed by some external intelligence. Thus the “God of the gaps” characterization.
Another proponent, William Dembski, claims that “specified complexity” is the key. Life, he says, is both “specified” and “complex”. By “complex”, he means very improbable, and uses a bunch of misplaced information theory to explain why the improbability is so great that it simply could not have been produced by natural forces. By “specified” he means…well, I’m not really sure what he means. Every "definition " I’ve read has been very vague at best, and unusable within any empirical methodology.
Both are fond of pointing to “the” bacterial flagellum (seemingly ignoring the fact that flagella come in many forms, some much simpler than others) as an example of either irreducible complexity or specified complexity. You can read a pretty good summary of both versions of the argument for design of the flagellum (as well as a rebuttal of both) here.
Also, note that the unifying theme of ID is that design is empirically detectable. A useful methodology for detecting this design has not been elaborated, however. There is also the underlying assumption that natural forces cannot produce the complexity seen in nature, and that materialistic metaphysics are therefore false (Dembski, for one, has outright stated that naturalism is false). In other words, like so-called “creation scientists”, they are attempting to use science to validate a metaphysic.
You can also see this Great Debates thread, among many others - just do a search for “intelligent design”, “Dembske” or “Behe”, and you’ll probably find lots of other definitions & critiques.
