Plural -s is a suffix, found in English and other related languages, which are added to the singular form of count nouns to form regular plurals. It acts as a grammatical marker for grammatical number.
Note that there may be some minor spelling changes. Words ending [C]y change to [C]ies, e.g. baby --> babies. Words ending in certain sounds take -es instead.
For the genitive form, to add the genitive 's morpheme, we add the apostrophe but not an additional s. e.g. "The teachers' holiday".
This suffix is notably also found in French and Spanish, some German words. In some French plural words this is an allomorph that is spelt -x, e.g. château - châteaux.
The plural marker can be confused, even by native speakers, with genitive 's, resulting in the infamous greengrocer's apostrophe.