It helps to take that in a slightly different order: There isn't really a particular person who says it. It's normally said to a person celebrating a birthday or other anniversary. It's a way of expressing the hope that they will have many more birthdays (or anniversaries), and that those will be happy occasions... in other words, "Happy Birthday, and I hope you have many more."
Usually said on your birthday. It is someone wishing you a long and happy life.
"Many Happy Returns" would be a somewhat silly response to "Happy New Year." The full phrase is "Many Happy Returns of the Day," and it's usually said to someone on their birthday (where it basically means "I hope you live a long time and all your birthdays are happy") or anniversary (meaning "I wish you a long and happy marriage").
This is the truncated version of "Wish you many more happy returns of the day", a greeting offered mostly on the occasion of someone's birthday. The greeting means that the recipient of the greeting may be blessed with a longer life.
Happy Returns - 1919 was released on: USA: 30 June 1919
In Kannada, "many happy returns of the day" is often translated as "ಹುಟ್ಟುಹಬ್ಬದ ಹಲವು ಹೋರಿಕೆಗಳು" (huttuhabbada halavu horikēgaḷu).
Many Happy Returns - 1913 is rated/received certificates of: UK:U
Many Happy Returns - 1916 is rated/received certificates of: UK:U
The duration of Many Happy Returns - TV series - is 1800.0 seconds.
Many Happy Returns - TV series - ended on 1965-04-12.
Many Happy Returns - TV series - was created on 1964-09-21.
Aloha: Hau'oli hoho'i nui [how-oh-lee hoho ee noo-wee]
The cast of Many Happy Returns - 1913 includes: Harry Buss as Father Josef