- the bike that belongs to Thomas is Thomas’s bike (not Thomas’ bike).
- the house that belongs to the Jones family is the Joneses’ house (but we are going to visit the Joneses).
- private parties, definitely not private party’s!
- ladies’ clothing, not ladie’s!
But what about today’s holiday honoring the world’s mothers? Or is it honoring YOUR mother and MY mother, uniquely and specifically? How you interpret the meaning determines where to place the punctuation.
The founder of Mother’s Day, Anna Jarvis, apparently was very specific about where the apostrophe belongs, in fact trademarking “Mother’s Day.” To her, the point was for each family to honor their mother.
However, as commercialization of the holiday has grown, the day is often interpreted to mean a celebration of all mothers. If that’s how you mean it, it would be “Mothers’ Day.”
Two bastions of grammar correctness – the Chicago Manual of Style and the AP Stylebook – both list “Mother’s Day” as the proper spelling. For now, especially because I love and honor MY mother first above all others, I’ll take their advice.