Let's break it down:
* Oui: This is the French word for "yes".
* Moi: This is the French word for "me".
* Aussi: This is the French word for "too".
So, the phrase literally translates to "Yes, me too".
It's often used to agree with someone who has just stated they like something, or are doing something.
For example:
* Person 1: J'aime le chocolat. (I like chocolate)
* Person 2: Oui, moi aussi. (Yes, me too)