Irreducible complexity is often illustrated with the analogy of a mousetrap. A mousetrap requires several parts to be correctly assembled in order to work. The removal or reduction of any part will result in the mousetrap not working.
Living organisms, much like a mousetrap, have irreducibly complex systems within them. This is a major problem for Evolution, because just as you cannot gradually remove pieces from an irreducibly complex system, you also cannot begin with reduced complexity and gradually build it up over time. But Evolutionists think they have resolved this issue: Add more mouse traps.
Evolutionists argue that biological systems cannot be irreducibly complex because there are other systems that do not work in the same way as the example in question. As an example, the reproductive system. This is an example I am especially fond of giving, because it is not just one system that must evolve, but 2, and they not only have to evolve to be fully functional, but fully compatible. A fully functioning male without a fully functioning female cannot reproduce, and Evolution ends with him. A fully functioning female without a fully functioning male also cannot reproduce, and so Evolution ends with her. Thus, reproductive systems, at least so far as we're talking about sexual reproduction, double the problem.
Not so, says the Evolutionist. Compare a human to a chicken. A human woman has a womb, a female chicken does not. A rooster doesn't have a penis, a man does. These are just two differences between the human and chicken reproductive systems. Thus, the human reproductive system is not irreducibly complex.
Except it is. All this alleged solution does is add a second irreducibly complex system to the mix, making the problem twice as large. Yes, there are multiple ways of doing the same thing, but that doesn't mean each of those ways can be reduced in complexity. There are multiple ways to trap a mouse, but swapping around the components of any mouse trap will inevitably result in multiple failures. In the same way, different organisms do have different ways of reproducing, but to alter their reproductive systems in order to make them more like that of another will result in failure to reproduce, and an end to Evolution.
As much as Evolutionists insist irreducible complexity has been refuted, the fact is it is unassailable. The existence of irreducibly complex systems, regardless of the variety they show, strongly suggests they were made by a very intelligent designer. Who is that designer? Only one being has ever been able to make a credible claim to that title: The Lord God of Israel.
The strongest evidence God presented to be the Creator is when He actually entered creation in the form of Jesus Christ. During His life, Jesus demonstrated power over creation that makes no sense if He was just an iron age carpenter. But if He really is the second person of the Holy Trinity, it makes perfect sense that He could control the weather, change the elements, heal the sick, and even raise the dead. Furthermore, though He Himself was killed rather brutally, it took Him a mere 3 days to get up and walk it off. But you ask, if Jesus is God, why was He so easily overwhelmed? Simple answer: He wasn't. Jesus went willingly to His death, because He was doing it out of love. Love, dear reader, for you.
See, the thing about human beings is we don't obey God like the wind and the waves do. More often than not, we disobey, and this disobedience is called sin. Sin, of course, deserves punishment, but it is a punishment we could never hope to bear: The second death. Eternal separation from God in Hell. But God doesn't want that, and so in punishing Jesus, who was innocent, He is able to forgive us, who are guilty. But only through faith. Confess Jesus as Lord, and believe He rose from the dead. Then, rather than receiving the just punishment for your sin, you receive eternal life in Heaven with your Creator.