This is the 4886th most frequent Russian word.
каждая
"Each" or "every" (feminine form).
Here, 'каждая' is used as a determiner to specify every single member of a set, which in this case is 'books on the shelf'.
Каждая книга на этой полке принадлежит библиотеке.
Each book on this shelf belongs to the library.
In this sentence, 'каждая' emphasizes individual contributions within a defined group, specifying individual ownership of actions within the subset of 'students'.
Каждая из учениц написала свои сочинения.
Each of the students wrote their own essays.
The word 'каждая' here emphasizes distinct occurrences of a recurring event within the timeframe, focusing on the 'meetings' happening over time.