Plain English Meaning
The direction that points the opposite way from where you are heading or looking. If you are heading one way, the reciprocal is the heading that takes you straight back.
Full Definition
The compass heading or bearing that lies exactly 180° opposite a given heading or bearing. The reciprocal of any heading is found by adding or subtracting 180°.
Context Anchor
Seen when setting or interpreting a course on a Horizontal Situation Indicator, and when comparing opposite runway directions or return courses.
Derivation
From Latin reciprocus, meaning 'moving backward and forward' or 'returning the same way.' That sense fits aviation use directly: the reciprocal heading is the one that would take you back the way you came.
Why Pilots Care
Confusing a heading with its reciprocal is a common navigation error. Flying the reciprocal of an intended course takes you 180° away from where you wanted to go. It also matters when intercepting a inbound versus outbound, and when reading the of an HSI instead of the head.