It literally translates to "for of me", but the more natural English translation is "for me".
Examples:
* "Un verre d'eau pour de moi, s'il vous plaît." (A glass of water for me, please.)
* "C'est un cadeau pour de moi." (It's a gift for me.)
The phrase is often used in situations where you are requesting something for yourself, or when you are explaining that something is intended for you.