An Irrational number is a number that you cannot represent with a fraction. For example, you cannot represent the number which you have multiply with its self to get 2 (square root of 2), its around 1.414, but it has infinite complexity. Some more examples of irrational numbers:
Many irrational numbers have special properities if you played with around them. Like how right-angled triangle with the longest side being the length of the square root of 2, the other sides will be 1 long. And how the space diagonal of a cube with side lengths of 1, is the square root of 3
There are two types of irrational numbers. There is algebraic numbers, which is a root of a non-zero polynomial (don't worry about what that means). And Trancendental numbers are numbers that aren't an algebraic number. An example of a transcendental number is Liouville consant (0.110001000000000000000001...)