Irreducible complexity is just a way of saying that for some systems, several key parts need to work together, or the entire system fails.
For instance, if the engine in your car is broken, you can’t drive it. The other parts of your car may be fine, but without the engine, the car as a whole is almost useless. Or if one of your wheels has been taken off your car, you can’t drive it, even if the engine is fine. In order to drive anywhere, the engine, wheels, and several other key parts need to be working at the same time. This is basically what irreducible complexity means.
In the creation vs. evolution debate, we use irreducible complexity to show why evolution is impossible. Evolution is supposed to be a slow, gradual process. Each small change helps an animal by a little bit, and slowly, over millions of years, animals develop complex machinery. There’s a major problem with this slow and gradual approach, however. Much of the “machinery” in animals could never be built slowly over time because it is irreducibly complex. Many parts need to be there at the same time for the system to work at all.
Let’s illustrate this point using a car again. If someone gave you a car without any wheels, what good would it do you? None. At least, it would do you no good as a vehicle to drive in. Or what if someone gave you a car without an engine? Again, it would do no good. There is no “slow and gradual” path for a car to evolve, at least not in regards to an engine or wheels. Both must be present for the car to work at all. A factory must create the car, fully functional from the start.
Likewise, many animals have irreducibly complex machinery. As Christians, we believe that God created these animals fully functional from the start, and this makes perfect sense with what we observe. Evolution, on the other hand, cannot make sense of this irreducible complexity.