Rough informal explanation. Because «меня» is a form of «я», into English it will be translated with “I” (but not always vice versa because of its other forms in Russian), while «мой» will be translated as “my” or “mine”.
Formally it can be explained like this:
«Меня» is a pronoun «я» (“I”) either in genitive (also called as possessive) or in accusative case.
«Мой» is possessive pronoun of “my”.
Some examples:
My phone → Мой телефон
I'm being dressed → Меня одевают
I'm absent → Меня нет