The most common uses of an apostrophe are to denote possession, as "Jim owns a house" would become "Jim's house," and in the merging of words known as contractions that are used for purposes of brevity and to reflect realistic dialogue. An example of the latter use of apostrophes would be "isn't" rather than "is not," or "aren't" in place of "are not." Contractions are generally not used in formal essays, but are, as noted, acceptable in more informal writing, as in speeches and when an author is depicting dialogues between characters.
Apostrophes used to denote possession in the case of plural nouns are placed after the "s," as in "veterans' parade," or, when referring to a family that possesses an object, "the Johnsons' car," which would be distinguished from a car owned by one member of that family: "Johnson's car." If there is one area in which the rule regarding apostrophes is a little muddled, however, it is in the case of proper nouns that end in the letter "s." A name that ends in "s," for instance, may or may not have the apostrophe separating an additional "s" to denote possession. For example, "Paris" (as in the city in France) might be written "Paris' weather," or, alternatively, could be written "Paris's weather." Many editors choose the former over the latter.
These, then, are the main uses of apostrophes. Possession and contractions are the principal applications of this particular punctuation mark.