A Fibonacci poem is based on the Fibonacci sequence 1,1,2,3,5,8,13,21...
The first and second lines are one word, the third line is two words, the fourth three and so on. You could change words to syllables, which i think is the original way of doing it. Here is an example from my class using words. I provided the first word.
(1) rain
(1) wet
(2) water falling
(3) it's quite cold
(5) I feel like a penguin
(8) I can jump in a very big puddle
(13) my mother: PUT ON 13 COATS! my father: TAKE AN UMBRELLA WITH YOU!