Meena's description of a relationship:
1. "my mother's husband" refers to Meena's father.
2. "my mother's husband's sister" is Meena's father's sister, her paternal aunt.
3. "the only son of my mother's husband's sister" is the only son of Meena's paternal aunt.
The son of an aunt is a cousin.
Specifically, the son of a paternal aunt is a first cousin (paternal cousin).
Conclusion: The man is Meena's cousin.
\[ \boxed{\text{Cousin}} \]