In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation:
Fn = (Fn-1) + (Fn-2), with seed values F0 = 0, F1 = 1
In English ... the series of numbers where the next number is the sum of the two preceding numbers.
Named after an Italian dude, Leonardo of Pisa, but known in Indian Math way before CACs (typical of most math) this sequence can be extracted from the Pascal's Triangle. Remember from HS math? Perhaps another in another thread.
That mathematical patterns are observed in nature obviously isn't ground breaking news, but it is pretty cool when you think about it in terms of the pervasive universality of math.