What does 讀書三餘 (독서삼여) mean?

ANSWER: reading's (讀書) three (三) leisure times (餘)

According to the ancient Chinese, the three best times to read were during the winter, at night, and during a rain. Why? Because the ancient Chinese were mostly farmers who had little leisure time, except during the winter, at night, and during a rain. The following Chinese idiom refers to these three leisure times:

讀書三餘 (독서삼여)

Reading's (讀書) three (三) leisure times (餘)

The ancient Chinese also believed that to truly understand a book or writing it should reach one's "mouth," "eyes," and "mind," and that means that one should read it aloud while focusing one's eyes and mind only on the reading. I assume that is why teachers in Joseon Korea's village schools (서당 書堂) would have their students read aloud the "Thousand Character Poem" (천자문 千字文) while focusing their eyes and minds only on the poem. If they failed to focus on the poem, the teacher would remind them to do so with his "teaching switch" (교편 敎鞭). The purpose was to have them become "absorbed in their reading" (독서삼매 讀書三昧). Anyway, the following Chinese idiom refers to the concept of "reading's three reaches":

讀書三到 (독서삼도)

Reading's (讀書) three (三) reaches (到)

Finally, the ancient Chinese believed that if you read or did something enough times, you will naturally come to understand it. That is why I like to read Korean books more than once, thinking that doing so will help me to better understand them.

讀書百遍義自見 (독서백편의자현)

[If you] read (讀) a book or writing (書) a hundred (百) times (遍), [its] meaning (義) will naturally (自) appear (見).