"Ti muži čekají na Kateřinu."

Translation: Those men are waiting for Kateřina.

[folshost]

What exactly would the difference be between this translation and "Those men are waiting on Kateřina"?

[va-diim]

"'Waiting on' somebody" has become more widely spoken in recent years because of the influence of hip-hop slang and bad grammar on proper English, but it's grammatically incorrect, unless referring to a waiter at a restaurant "waiting on a customer." The proper grammar in the other context is "'waiting for' somebody."

[ion1122]

va-diim is correct. Until recently, using 'wait on' in place of 'wait for' was considered substandard. Even today it would be flagged as incorrect in a university paper.

[sanquii]

I believe both are acceptable in English.

[kid-a-10]

Is there a difference between Kateřina and Kateřinu? Why is it written like that, or is it a typo?

[va-diim]

After the phrase čekají na, "are waiting for," the name takes the accusative case. Here's a chart of all the cases for the Czech name.
https://en.m.wiktionary.org/wiki/Kate%C5%99ina#Declension