Let's break down the relationship described by Meena:
1. "my mother's husband": This is Meena's father.
2. "my mother's husband's sister": This is Meena's father's sister. Meena's father's sister is Meena's paternal aunt.
3. "the only son of my mother's husband's sister": This is "the only son of Meena's paternal aunt".
The son of one's aunt (either paternal or maternal) is one's cousin.
Specifically, the son of a paternal aunt is a first cousin (paternal cousin).
Therefore, the man is Meena's cousin.
\[ \boxed{\text{Cousin}} \]