"Irreducible complexity" essentially means that a usefully functioning, complex component of an organism can have no possible useful function if any of its parts are removed. This concept leads directly to the conclusion that the component must have come into being as a completely new, fully functional, complex organ or organelle, without any gradual evolution from earlier, less complex systems (which would not have had any useful function). This, in turn, leads to the conclusion that any fully functioning, complex component cannot have evolved because evolution is, by definition, a gradual accumulation of small mutations, as opposed to the sudden appearance of a completely new, fully functional, complex organ or organelle.
The concept of Irreducible complexity is vital to Intelligent Design theory because it it is the basis for the assertion that an organism is too complex to be just the result of a series of random, isolated mutations; one that came into existence independently of any organizing agent.
While Creationists have used the arguments put forward by Professor Behe it is worth remembering that he himself does not specifically point to creation but is only seeking to object to evolution and demonstrate its impossibility. Having said that it is easy to see why Creationists find much on common with intelligent design. Professor Behe has put forth a number of examples that purportedly demonstrate systems or organs that simply could not work unless the system or organ came into existence as a whole; in other words, that the individual parts simply could not work alone, and that therefore all the parts must somehow have "fallen into place" simultaneously for the system to provide any survival advantage to the organism.
It has been argued that one of Darwin's motivations was specifically to refute William Paley's argument from design. Behe has in a sense turned the tables on Darwin and demonstrated why unguided evolution, in his opinion, cannot work. Creationists would argue effectively that creation by an intelligent designer is tantamount to arguing for an intelligent Creator viz. the God of the Bible.
Many scientists have presented arguments that, they assert, refute the concept of irreducible complexity. The primary argument against irreducible complexity is the process, observed in nature, of exaptation, wherein an existing organ or system confers a survival skill other than that for which it originally evolved. One example of this that has been cited in the scientific journals is the development, in bacteria, of a secretory system (to secrete fluids) that, at a certain point in its development, also had the side-effect of causing the bacterium to move about, but in a useless, random fashion. This facility for random movement then, scientists assert, independently evolved into a functional system for directed, non-random movement, and currently exists as what is called the "flagellum" - the organ the gives bacteria the ability to move about. The existing flagellum would seem to have no effective function if any of its parts were removed; nonetheless, a potential mechanism for its evolution has been presented, thus, presumably, refuting the concept of irreducible complexity.
The following links provide details of some of the arguments and discussion surrounding Behe's irreducible complexity idea from a Creationist perspective. Also included is the "Wikipedia" article on irreducible complexity.
