It's the contraction of "avec" (with) and "ma" (my), which is the feminine singular form of the possessive adjective "mon" (my).
Here are some examples of how it can be used:
* Avec ma famille (with my family)
* Avec ma voiture (with my car)
* Avec ma sœur (with my sister)
* Avec ma meilleure amie (with my best friend)
* Avec ma permission (with my permission)
The specific meaning of "avec ma" will depend on the context of the sentence.