In French, "mon" is used for singular masculine nouns (e.g. Je déteste <u>mon</u> frère) or any singular nouns that begin with a vowel or silent h (e.g. J'aime discuter avec <u>mon</u> amie Julie) when speaking in the first person.
The other options:
mes = my; plural first person
ma = my; feminine (when the noun does not start with vowel/silent h) first person
m' = not commonly used. You may see it in words like m'appelle but don't worry about it, mon will be used for words that start with a vowel/silent h.