To study hard or begin studying seriously, especially for an exam or academic assignment.
This American student slang emerged in the 1930s-1940s, during a time when "hit" was commonly used to mean "to go to" or "to start doing" something energetically. The "books" obviously refers to textbooks and study materials, making this a straightforward metaphor for attacking one's studies with vigor.
The violent imagery of "hitting" books perfectly captures the aggressive, determined approach that serious studying often requires. It's interesting how this phrase makes studying sound almost like a physical battle - which anyone who has crammed for finals knows it sometimes feels like!
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