To “hit the books” means to study them. There are many other “hit” sayings; “hit the sack” and “hit the hay” both mean to go to bed, and “hit the gym” means to go to the gym (to work out).
 
“Hit the books hard for short but, for him, weary intervals” was cited in 1911. A 1928 newspaper story about Princeton University slang stated that “to ‘hit the books’ is to spend an indefinite period of hard work at studying.”
     
 
Wiktionary: hit the books
Verb
hit the books
1. (idiomatic) To study, especially with particular intensity.
 
29 January 1911, Tulsa (OK) Daily World, “News Notes from State University,” pg. 6, col. 3:
If he be of the indolent kind, he will for this once find the impulse to “dig” upon him and hit the books hard for short but, for him, weary intervals.

5 October 1923, The Daily Northwestern (Evanston, IL), ““Unconquerable Fight,” pg. 2, col. 1:
Because we believe the student in a university today should consider these attributes of the conqueror. He need not hit the line of an opposing gridiron team to need them; instead he will find that to “hit the books,” and be a good student requires the qualities.
 
17 January 1928, The Capital Times (Madison, WI), “Missed Free Throws Cost Cards’ Game,” pg. 12, col. 7:
The Cardinal cagers will hit the books until just before their tilt with the strong Irish five. It is hoped that both Tenhopen and Miller will be eligible to compete the second semester, ...
 
19 May 1928, Trenton (NJ) Evening Times, “Princeton ‘Lingo’ Highly Developed,” pg. 3, col. 6:
To “hit the books” is to spend an indefinite period of hard work at studying.
   
Google Books
16 November 1987, New York magazine, “Against All Odds” by Barbara Campbell, pg. 71, col. 2 photo caption:
HITTING THE BOOKS: Tanya, an A student, does her homework on her bed.
 
OCLC WorldCat record
Hit the books! Here’s how to get the professional education you need to advance your career
Edition/Format: Article Article
Publication: TRAFFIC MANAGEMENT, 33, no. 2, (1994): 42
Database: British Library Serials
 
OCLC WorldCat record
Hit the Books - In our annual survey, we examine our readers’ reading habits.
Author: June Culp Zeitner
Publisher: San Diego, Calif. [etc.] Lapidary journal.
Edition/Format: Article Article : English
Publication: The Lapidary journal. 49, no. 8, (1995): 65
Database: ArticleFirst
 
English Idioms
Sunday, May 29, 2011
Hitting the Books
To “hit the books” is to devote yourself to study. This is as opposed to hitting the hay (going to sleep).
 
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The new school year is just 10 days away. Who’s ready to hit the books? #IAmAHillcat #HillcatNation
12:33 PM - 7 Aug 2015
Claremore, OK