Plain English Meaning
Working out what is wrong with something by checking the most likely causes one at a time until the real problem is found.
Full Definition
A systematic process of identifying the cause of a malfunction in an aircraft system or component by observing symptoms, isolating possible sources, testing each in a logical sequence, and confirming the fault before repair.
Context Anchor
Seen in aircraft maintenance, preflight problem reports, and discussions between pilots and mechanics when something does not operate as expected.
Derivation
From 'trouble' (problem, fault) plus 'shooting' in the older sense of 'going after' or 'pursuing.' The word entered industrial use in the early 1900s for tracking down faults in telegraph and electrical systems. The aviation meaning carries the same idea: hunting down the of a problem.