The story
From being an engine burn whose failure results in destruction, thus seemingly requiring "suicidal" confidence or courage to attempt.
Etymology from Wiktionary, CC BY-SA 4.0.
suicide burn
Today it means: A method of soft-landing a rocket with a well-timed, high-thrust engine burn starting at the last possible second, such that it reaches a vertical speed of zero at precisely or almost precisely at the exact moment that it touches the landing pad and the engine shuts down. Full definition →