A possessive noun is a noun that possesses something—i.e., it has something. In most cases, a possessive noun is formed by adding an apostrophe +s to the noun, or if the noun is plural and already ends in s, only an apostrophe needs to be added. In the following sentence, boy’s is a possessive noun modifying pencil: The boy’s pencil snapped in half. It is clear that the pencil belongs to the boy; the ’s signifies ownership.
The cat possesses the toy, and we denote this by use of an apostrophe + s at the end of cat.
When a noun ends in the letter s or an s sound, the same format applies. This is a matter of style, however, and some style guides suggest leaving off the extra s.
Plural nouns ending in an s simply take an apostrophe at the end to form a possessive noun. Of course, there are many plural nouns in English that are irregular and do not end in s.
For more examples on how to use apostrophes to form possessives, read Apostrophe.