The binomial inverse theorem is about how two different things can be swapped around. It says that if you start with two things (called x and y) and you combine them in some way, then you can swap the two things to get back what you started with. An example of this is multiplying two numbers together then taking the square root. If you start with 2 and 4 you end up with 8 (2 x 4). Now if you take the square root of 8 you get 2 and 4 again (the square root of 8 is 2 and 4). This is what the binomial inverse theorem says - that you can swap the two things and still get the same result.