The phrase is used to express a sense of achievement and pride, similar to displaying a trophy. After years of hard work, getting that promotion was a feather in your cap.
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Metaphoric Origin
Historically, warriors added feathers to their hats for each victory, representing success. Securing the deal with the client felt like adding a feather in your cap.
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Casual Use
Best used in informal or colloquial settings, rather than in very formal or academic writing. Completing the marathon was a real feather in your cap, wasn't it?