This is the 11953rd most frequent Polish word.
kuzyn
"Cousin" (male).
Here, 'kuzyn' refers to the speaker's male cousin, and the sentence identifies his place of residence.
Mój kuzyn mieszka w Krakowie.
My cousin lives in Kraków.
In this question, 'kuzynem' is the instrumental case of 'kuzyn', used because of the verb 'spotkać się' (to meet).
Czy spotkałaś się z moim kuzynem?
Have you met my cousin?
Here, 'kuzynem' is again in the instrumental case, following the verb 'rozmawiać' (to talk).