Irrational Numbers are numbers that cannot be expressed as a fraction, where both the numerator and denominator are integers.
Above we have an irrational number, and a rational number. The square root of "2" cannot be expressed as a fraction. The numbers after the decimal continue on forever. The square root of "5" can be expressed as a fraction (5/1, 10/2, 15/3, etc). The numbers after the decimal terminate.
Real Numbers are defined as the combination of all rational numbers and irrational numbers.