The phrase is informal and often used in casual or humorous contexts, not usually in formal settings. In our club, Jenna is considered the big cheese because she's been there the longest.
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Slightly Humorous
'A big cheese' can suggest a playful or ironic recognition of someone's importance or influence. You’ll have to ask Mark, he’s the big cheese around here when it comes to scheduling.
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Non-Literal Meaning
It doesn't refer to cheese at all; it's a metaphorical expression for a person's status. After the promotion, everybody treated him like the big cheese of the department.