Background: what a lady may not wish to reveal about it (8)
'background' is the definition.
(as in someone's national or ethnic background)
'what a lady may not wish to reveal about it' is the wordplay.
'what a lady may not wish to reveal' becomes 'herage' (traditionally it is rude to ask a woman her age).
'about' is an insertion indicator.
'herage' going around 'it' is 'HERITAGE'.
(Other definitions for heritage that I've seen before include "That which is passed down from ancestors", "Their age (anag.)", "Our historic legacy", "Objects and cultural traditions passed down", "Ancestry".)