Ah, its so easy for you fellow Slavs, so many words and roots of words in common!
However, what do you do when "godzina" means "hour" in Polish and "godina" means "year" in Serbian? :D More examples: https://en.m.wikibooks.org/wiki/False_Friends_of_the_Slavist
How would one pronounce the "h" and "v" sound next to one another? Does this end up sounding like an "f"?
I believe something like "your 15 minutes" (usually 5 in Polish), as Andy Warhol talked about.
Could it be "this is your turn," as in time to play a card, or do one's individual performance?
Not really, maaaybe the 'individual performance' but still on the level of 'your 15 minutes' rather than a normal phrase.
"your turn" is "twoja kolej".