This is the 1288th most frequent Polish word.
kolejnego
"Kolejnego" means "next" or "another" in English, depending on context.
Here 'kolejnego' refers to an item in a sequence, the next train, modifying 'pociągu' also in the genitive case.
Czekam na przyjazd kolejnego pociągu.
I am waiting for the arrival of the next train.
Here 'kolejnego' is used as an adjective in the genitive case to describe 'deseru', meaning 'another'. It signifies a sequence rather than merely doubling.
Zjadłem pełny obiad i zamówiłem kolejnego deseru.
I ate a full lunch and ordered another dessert.
In this context, 'kolejnego' modifies 'dnia' in the genitive case, signifying the upcoming instance in a calendar.