In writing Mother's Day, I reminded you that the day belongs to one mother--your mother. Thus, you write Mother, then you show possession to the word mother: Mother's Day.
Possession can be so tricky because we think of whether the word is singular or possessive; we contemplate whether the apostrophe should be on the inside or outside of the s, etc. It doesn't need to be that complicated! You are probably thinking too hard!
Tricky Trick to Help It Stick: Do not worry about whether the word you want to show possession to is singular or plural.
1. Just write the word you want to show possession to
2. Then see if it does or does not end in an s:
a. If it DOES end in an s, just put apostrophe on the outside of the s that is already there (s')
ii. glass' rim
b. It it does NOT end in an s, add apostrophe s ('s)
ii. cup's rim