The hawks fly and the fish leap; describes the natural freedom of all living things to act according to their nature and flourish in their environment.

fish leaping in a deep pool; a metaphor for living things thriving in their natural environment and being content in their proper place

Based on the legend of a carp jumping over the Dragon Gate to become a dragon, it is used as a metaphor for passing a high-level exam or achieving a sudden rise in social status.