Michael Behe introduced the term "irreducible complexity" for systems composed of interacting parts in which removal of a necessary component causes the system to lose its basic function. The bacterial flagellum became one of the best-known examples in the Intelligent Design debate.
The argument is not simply that a system is complicated. It asks whether a functional evolutionary pathway exists in which earlier stages can perform useful functions before the complete modern system is present.
Some molecular systems do depend upon numerous coordinated components. The flagellum requires structural, regulatory, assembly, and motor functions. Intelligent Design advocates argue that such interdependence creates a significant explanatory problem for gradual evolutionary accounts.
Loss of the present function when a component is removed does not prove that earlier forms could not have possessed different functions. Co-option, redundancy, scaffolding, gene duplication, and changes in function can potentially produce pathways that are not revealed by simply removing parts from the modern system.
Can proposed evolutionary histories demonstrate plausible and sufficiently supported functional stages for systems claimed to be irreducibly complex?
Irreducible complexity is most useful as an investigative question rather than a shortcut to a design conclusion. It directs attention to the origin of coordinated function and asks whether proposed natural pathways adequately explain the system rather than merely asserting that a pathway must have existed.