The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.  Each number in this sequence is simply the sum of the two preceding numbers, and sequence continues infinitely.
Fibonacci's sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series. For reasons that are unclear, these ratios seem to play an important role in the stock market, just as they do in nature, and can be used to determine critical points that cause an asset's price to reverse. 
From Leonardo Fibonacci (1170 - 1250AD), The Italian mathematician who discovered the series.