Me is the object form of I.
Direct Object of a verb: That big boy hit me! (“me” is an object because it receives the action of the verb “hit.”
Indirect Object of a verb: Give me that small piece of cake. (“me” is the indirect object of the verb “give” because it receives the “cake” which is the direct object of the verb “give.”)
Object of a preposition: The cat is sitting on me. (“me” follows the preposition “on.”)
The same functions apply to the other object forms of the personal pronouns him, her, us, and them:
Direct object of a verb:
That boy hit him.
That boy hit her.
That boy his us.
That boy hit them.
Indirect object of a verb:
Give him a piece of cake.
Give her a piece of cake.
Give us a piece of cake.
Give them a piece of cake.
ERROR ALERT: The most common error associated with the rules that apply to the object forms of the pronoun is to use a subject form where the object form is called for.
Non-standard usage: They invited Sally and I to the White House.
Correct standard usage: They invited Sally and me to the White House.
