Hit the Books means: To study.
Example of use: “Danny was in danger of failing, so before his last math test he left the show early to go home and hit the books.”
In this phrase, hit means to start or to begin. Although no one knows the origin of the idiom “hit the books”, it seems to be related to early idioms such as “hit the trail,” which cowboys used when starting out on a journey. It’s clear that this saying is a fairy contemporary one, probably from the mid-20th century.