I dont understand the whole immortality thing. Can someone explain?

In legends it is said that if you eat the flesh of a mermaid you will become immortal.

Mermaids are supposed to be immortal creatures but in this story they can undo that immortality by mating with a human. That human in turn becomes immortal but the mermaid dies after a normal lifespan. Supposedly the child born from the two is human but I'm still hazy on that aspect.