An apostrophe after an -s usually is used to convey a plural word's possessive form.
Though an apostrophe is used to indicate anything's belongingness, its use after -s is different.
Give your parents' contact numbers.
In this sentence, parents refer to both father and mother. So, it's a plural form and to convey the idea of this plural word's possessiveness, the apostrophe is used after the -s.
N.B. If we use the apostrophe before -s (parent's contact numbers), it would imply the contact number(s) of any of the parents.