Outside of LessWrong, "humility" usually refers to "a modest or low view of one's own importance". In common parlance, to be humble is to be meek, deferential, submissive, or unpretentious, "not arrogant or prideful". Thus, in ordinary English "humility" and "modesty" have pretty similar connotations.
On LessWrong, Eliezer Yudkowsky has proposed that we instead draw a sharp distinction between two kinds of "humility" — social modesty, versus "scientific humility".
In The Proper Use of Humility (2006), Yudkowsky writes:...