A series of numbers, such as "1, 1, 2, 3, 5, 8,..", in which each number is the sum of the two preceding ones. See also "456,456,912,1368,2280,3648,..." This phenomenon is names after the name given to Leonardo of Pisa (1200), a Tuscan mathematician.
...and if you divide each number by the one before it, the result gradually converges towards 1.6180339887..... and if you divide each number by the one after it, the result converges towards 0.6180339887.... which is one less than the reciprocal.
If you are interested, there's a novel called The Da Vinci Code by Dan Brown which has the Fibonacci series as part of the clues in solving the mystery - it's really good! (I think - don't hold it against me if you hate it........)