This is the 9452nd most frequent Polish word.
warszawskim
"Warszawskim" means "Warsaw-related" or "of Warsaw" in English, referring to something associated with the city of Warsaw.
In this sentence, 'warszawskim' is used as an adjective to describe the location of the market square as being in Warsaw.
Spotkaliśmy się na warszawskim rynku.
We met at the Warsaw market square.
Here, 'warszawskim' modifies 'klubu sportowego' (sports club), indicating that it is based in Warsaw.
Jestem członkiem warszawskiego klubu sportowego.
I am a member of the Warsaw sports club.
In this case, 'warszawskim' describes the university, specifying its association with Warsaw.