A young boy gets saved from drowning by a mermaid, but according to mermaid law, if a human sees a mermaid's true form, both have to be killed. The only solution to the problem is for him to marry her.
You can read more about the acquisition on another ANN page and more on the characters and story on Wikipedia. We'll certainly be getting a copy of it for our respective collections. In the meantime, despite the fact that we can't read or understand Japanese we think this is a promo from the first episode of the television series. Our minor frustration – NOT ENOUGH MERMAID TAIL! – which is why we promise you nothing but tails in Elf~Fin.