introducing a man, a woman said, he is the only son of the mother of my mother. how is the woman related to the man?

Let's analyze the statement step-by-step:

• The woman says: "He is the only son of the mother of my mother."
• "The mother of my mother" means my maternal grandmother.
• The "only son of my maternal grandmother" would be the woman's maternal uncle (her mother's brother).

Conclusion:

The man is the woman's maternal uncle. So, the woman is the niece of the man.