The saxon genitive is the traditional term used for the "'s" word ending in the English language. The term is now infrequently used by linguists who argue that "'s" represents a possessive, not a genitive. And moreover the "'s" now functions as a clitic rather than a case ending.

Modern English forms the saxon genitive as follows

         Regular noun          Regular noun      Irregular nouns
         not ending in "s"     ending in "s"

Singular    's                 's                 's         

Plural      s'                 es'                's

Example   cat's                pass's             child's 
          cats'                passes'            children's

Pronouns do not combine with "'s" to form possesives; there are a range of Possessive pronouns used instead.

In Old English nouns declined according to grammatical gender. The modern saxon genitive is derived from the strong masculine genitive case of Old English. The plural forms are a relatively modern innovation, and are not derived from Old English

Gender               Singular          Plural

Strong masculine     -es               -a

Weak masculine       -an               -ena

Strong feminine      -e                -a

Weak feminine        -an               -ena
 
Strong neuter        -es               -a

Weak neuter          -an               -ena

The term "saxon genitive" is in analogy to the genitive in classical Latin.