It means that a cinema pays money a company for showing its movie (кинолента)

Thanks for the clarification, Эдуард. снимать is one of these russian verbs whose I don't understand the logic: so many significations for only one verb :)

i can refer to any thing you hire - a car , a suit .... взял машину на прокат, взяли свадебное платье на прокат. but if you rent an apartment - you need to say - снитать квартиру