As mgb_phys posted a complex number is a number of the form c = a + id. As the link that Borek posted indicates in the a+di form a and d are real numbers and i is the imaginary number (the square root of -1). Here a is called the real part of c and d is called the imaginary part of c.
Complex numbers are important for many mathematical functions such as solving roots of polynomials, transcendental functions, etc. They can be easily represented programmatically as a named pair of floating point numbers representing the real part and the imaginary part, so they form a kind of prototypical example of a structured data type.
Your reply to Borek was not very polite. He correctly identified your question and pointed you to a good site to fully answer it. He did not deserve to be replied to in that fashion.