"Irreducible Complexity" is a concept mainly used by the advocates of Intelligent Design aka Creationism. It states that something complex, like a bacterial flagellum (which is the advocates' favorite example), can't function the same way if some parts are removed from the whole, thus it can only be created through design, thus disproving evolution.
Take a significant part from the whole and the system ceases to function. Take the wheels out of a car; it wouldn't work the way it is intended. Take the engine out, it still wouldn't work. The car will only work if all the pieces are in place. The car is irreducibly complex.
I don't subscribe to this belief. Why?
The concept of irreducible complexity is an insult to amputees, the mentally challenged, the disabled, and anyone lacking fully functional organs or appendages that would deem you complete. More often than not, these individuals with disabilities can perform just as well or even better than people who have no disabilities. Artists without hands, athletes without feet, idiot savants... we all heard of these. They don't consider their disabilities as hindrances.
Furthermore, Irreducible Complexity opposes the concept of "Multiple Intelligence" wherein humans are classified according to their talents and abilities, which obviously differs from each human. Someone may be good at music and be bad at math. That doesn't make them less of a human being than someone bad at music and good at math. From what standard do we get the "control sample" of the "normal" intelligence and talents of a human being?
From this, I can say that Irreducible Complexity is definitely incorrect. The existence of disabled humans doing well with what they do is the hard evidence against it.