Usually a chicken dish represents the phoenix. Lobster or sometimes eel can represent the dragon. Also a "cold platter" of jellyfish and various meats arranged in dragon and phoenix shapes may also be served.
This soup uses a particular type of seaweed (fa cai) called "black moss" in English. This type of seaweed looks like strands of black hair. The soup is supposedly very nourishing for the new mother and the guests. And "fa cai" is also a Chinese homonym for "prosperity."