Let's break it down:
* Al fin: This means "finally" or "at last."
* Te entiendo: This means "I understand you."
* Prima: This is the feminine form of "primo" which means "cousin."
So, the entire phrase expresses a feeling of understanding and connection with a female cousin.
It implies that the speaker has finally grasped the cousin's perspective, perhaps after a period of misunderstanding or disagreement.