Irrational numbers are real numbers that cannot be expressed as a simple fraction, meaning they cannot be written as the ratio of two integers. Examples of irrational numbers include π (pi), which represents the ratio of a circle's circumference to its diameter, and the square root of 2, which cannot be simplified into a fraction. These numbers have non-repeating, non-terminating decimal expansions. This means that when you write them as decimals, they go on forever without repeating a pattern. Irrational numbers are important in mathematics and appear in various fields, including geometry and calculus.