When it's not a contraction it's about possession. But it's really not that simple. Here's a source that attempts to explain all the cases.
Apostrophes with Names Ending in s, ch, or z
Are you confused about how to show the plural and the possessive of certain names? Maybe you know to write I met the Smiths, I drove Brenda Smith’s Ferrari, and I visited the Smiths’ house. But what if the name is Sanchez or Church or Williams?
Rule: To show the plural of a name that ends with a ch, s, or z sound, add es. If a name ends in ch, but is pronounced with a hard k sound, its plural will require s, rather than es.
The Sanchezes will be over soon.
The Thomases moved away.
The Churches have arrived but the Bohmbachs are running late.
Rule: To show singular possession of a name ending in ch, add ’s on the end of the name.
Harry Birch’s house
Rule: To show singular possession of a name ending in s or z, some writers add just an apostrophe. Others also add another s. See Rules 1b and 1c of Apostrophes for more discussion.
Bill Williams’ car OR Bill Williams’s car
Mrs. Sanchez’s children
Rule: To show plural possession of a name ending in s, ch, or z, form the plural first; then immediately use the apostrophe.
the Williamses’ car
the Birches’ house
the Sanchezes’ children
But it's not even that simple as explained in: Is “ ’s ” ever correct for pluralization?
And the name itself can change the way you should show possession, as explained here: Which singular names ending in “s” form possessives with only a bare apostrophe?