The Fibonacci sequence is a series of numbers where each subsequent number is the sum of the previous two. It was introduced to Western mathematics in 1202 but was originally created by Indian mathematicians 1300 years ago. The sequence follows the pattern: 1, 1, 2, 3, 5, 8, 13, 21, etc. To generate each new number, you add the two numbers before it - for example, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on. The Fibonacci algorithm uses variables P, C, and N - where P stores the previous number, C the current number, and N calculates the next number as P + C.