In the sentence, "The cat's toy is pink," the word "cat's" is the possessive noun. In the phrase, "America's freedom," the word "America's" is the possessive noun. Singular, possessive noun forms are used to show that one (singular) person, place, or thing (noun) has ownership or possession of something else.
Some examples of singular nouns in the possessive case are known as possessive pronouns. Some examples of possessive, singular pronouns include, "yours," "hers," "his," and "mine." Note that singular, possessive pronouns do not include apostrophes.
Other singular possessive nouns can be proper nouns, which refer to the names of people or places. Possessive proper nouns include "Johnny's" and "Rome's."
Possessive singular nouns, except for pronouns, are special in the English language because of their punctuation. The apostrophe is what distinguishes the singular possessive form of a noun from the plural form. For example, the sentence, "Cats are solitary" demonstrates the plural form of the word "cat." The sentence, "My cat's antics are hilarious" demonstrates the possessive singular because of the apostrophe added before the letter "s."
Singular possessive nouns that end in the letter "s" may be punctuated differently than other nouns. For example, in the phrase, "In Jesus' name," the apostrophe may be used without the ending "s." Some style manuals, such as the Chicago Manual of Style, as of 2015, may allow the use of the extra "-s," resulting in "in Jesus's name."