Why is 秘书 (lit. "secret book") the Chinese word for "secretary"?
秘 = secret --> private 

书 = 书记 = clerk; secretary

秘 has the meaning of 'secret' , and it extends to 'private'

书 in 秘书 doesn't mean book, it is short for 书記 (clerk; secretary), a job title. 

In fact, another common translation of 'secretary' is "书记" as in  "党书记" ( Party secretary)

秘书 is literally a "private secretary"

书记 can be working for a department or for one person, to differentiate the two, we also have the term 私人书记 (personal clerk) = 秘书 (private  secretary)