These days it is more common for people to say ‘Happy Birthday‘, but you still sometimes hear ‘Many Happy Returns’. A student asked me the other day what this phrase meant, as it is not obvious to foreign speakers.
The full phrase was originally ‘many happy returns of the day’ and was used on any festive occasion – birthday, Christmas, New Year. Since the 19th century it has been used primarily for birthdays. It means that the wisher hopes the wishee has many more of these special days.