Here's the breakdown:
"mich" is the accusative case of the personal pronoun "ich" (I). It's used as the direct object of a verb.
"mir" is the dative case of the personal pronoun "ich" (I). It's used as the indirect object of a verb, or to indicate possession.
Here are some examples:
* "Der Hund beißt mich." (The dog bites me.) - "mich" is the direct object of the verb "beißen".
* "Gib mir den Ball!" (Give me the ball!) - "mir" is the indirect object of the verb "geben".
* "Das Buch gehört mir." (The book belongs to me.) - "mir" indicates possession.
In short:
* "mich" is for "me" as the direct object.
* "mir" is for "me" as the indirect object or for possession.
Remember, German uses different cases for pronouns depending on their function in the sentence.