The noun "Homer's" (capital H) is a proper, possessive noun; a
word indicating that something in the sentence belongs to someone
named Homer.
Example: We're spending the holiday at Uncle Homer's farm.
The noun "homer" (lower case h) is an informal word for a home
run in baseball. The possessive form, "homer's" indicates that a
noun in the sentence is related to that noun.
Example: The homer's crack against the bat brought a cheer from
the stands.