The sequence start at zero which is added to the number one to give a sum of one you add that sum to the nest number which is one plus one equal two. That takes us to the next which is one plus two equals three. Two plus three result in five and three plus five equals eight.
Now eight is a interesting number you turn it on its side and you get the infinity symbol. In numerology eight meaning is strength of will endurance through any thing the will of the soul. a very powerful number.
Next in the series is five plus eight which gives us 13. We no add eight and 13 to get 21. We now come to another interesting phenomena, when you divide 13 into 21 you get a result of 1.6350… which is pretty close to the golden mean a ratio of 1.618.. the golden mean is at the heart of beauty and symmetry and the natural world. the Greek lauded it as most important number. Artist use it such as Leandro Di Vincci most notable.
As I understand it the Fibonacci series is closely tied to the Golden mean which is closely tied to everything we hold to be beautiful. Oh and one more thing about this series it mathematically describes the spiral which is how almost everything in this universe goes in. We do not circle the sun which is moving in an arm of the milky way galaxy at an incredible speed we spiral around it as the star do around the galactic core. So the Fibonacci numbers are at the heart of creation its self.