To accept responsibility for something you have done wrong and deal with the unpleasant consequences that follow.
The phrase emerged in American English around the 1850s and has maintained its meaning of confronting unpleasant consequences with courage. Whether from military or theatrical origins, it emphasizes the idea of standing up straight and facing whatever comes next.
What's compelling about this phrase is how it transforms a potentially cowardly moment - running from consequences - into an act of courage and dignity. The musical metaphor suggests there's almost a rhythmic, inevitable quality to facing up to what you've done.
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