Plain English Meaning
A small flag on the HSI that pops into view to tell the pilot the heading shown by the instrument cannot be trusted right now.
Full Definition
A warning flag on a Horizontal Situation Indicator (HSI) that appears when the heading information being displayed is unreliable or has failed. When visible, the HSI's heading display should not be trusted for navigation or course tracking.
Context Anchor
Seen on an HSI or other cockpit heading display when the heading source or signal has failed or is not usable.
Derivation
HDG is the standard cockpit shorthand for heading. A 'flag' in instrument terminology is a small visible indicator that drops into view to warn the pilot of a problem — the same idea as a red flag being raised to signal a fault.