This is the 752nd most frequent Polish word.
cały
"Cały" means "whole," "entire," or "all" in English.
In this sentence, 'cały' is used as an adjective in its masculine singular form to mean 'entire' or 'whole' and modifies the noun 'dzień' (day). It emphasizes that the action lasted throughout the entire day.
Cały dzień padał deszcz.
It rained the entire day.
Here 'całą' is the accusative form of the feminine singular adjective 'cały,' modifying 'książkę' (book). It indicates that the entirety of the book needs to be read, without any part left out.
Mam całą książkę do przeczytania.
I have the whole book to read.
In this instance, 'całości' is the instrumental singular of 'całość,' a noun derived from 'cały,' meaning 'entirety' or 'wholeness.' It conveys the sense of experiencing everything as a complete unit.