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 "One comes into this", "Objects and cultural traditions passed down", "Birth-related condition", "historical collection?", "Property or practices passed down".)