As a noun, grandstand means a large seating area for sports spectators. As a verb, it means to show off. So if you dance around in a banana costume at the horse races, you grandstand in the grandstand.
Tiered, covered seating at a racetrack or outdoor sports arena is one kind of grandstand. This word has been used since the mid-18th century, and in the late 1800s it was adapted into the baseball slang phrases grandstand player and grandstand play, which referred to theatrical, unnecessary moves athletes made simply to show off. These terms found their way into college slang around the same time, and grandstand became a common way to say "put on airs."
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