In common parlance, "humility" refers to "a modest of low view of one's own importance". To be humble is to be meek, deferential, submissive, or unpretentious, "not arrogant or prideful". Thus, in ordinary language "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 "epistemic humility" or "scientific humility".
In The Proper Use of Humility (2006), Yudkowsky writes:...