A Fib is kind of like a haiku, in that there's a specific number of syllables in each line. In this case, it follows the pattern of the Fibonacci Sequence, where each number in the sequence is the sum of the previous two numbers. The poems usually have 6 lines, so the syllables per line are 1, 1, 2, 3, 5, and 8.
Here's a bad example I just came up with:
This
is
a nice
place to spend
some time if you have
creativity and humor.
I'm sure the Mellos can do better.