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.
Examples:
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.
Example:
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.
Examples:
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.
Examples:
the Williamses’ car
the Birches’ house
the Sanchezes’ children
grammarbook
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?