For example
Wenn jemanden etwas stört, sagt er's offen und direkt
How is this different
Wenn jemanden etwas stört, sagt er offen und direkt
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Wenn jemanden etwas stört, sagt er's offen und direkt
How is this different
Wenn jemanden etwas stört, sagt er offen und direkt
The verb sagen is transitive in German, just as "to say" is transitive (for most meanings) in English. In other words you have to mention what is said, even if it's only with a pronoun. So in English, you'd have to include the "it" in "If something bothers someone, they say it openly and directly." Similarly, German allows you to contract the es to 's, but as noted in the comments, dropping it entirely sounds wrong, even if the meaning is clear.
In "er's", the apostrophe marks the omission of letters, it replaces "... er es".
A similar use of the apostrophe exists in English, e.g. "it is" -> "it's" or "do not" -> "don't".
On Wikipedia you can find an explanation of the uses of the apostrophe in the German language (in German).