A quick cleaning or polishing with a brush, or a quick review or improvement of skills.
Noun formed from verb phrase 'brush up' (meaning to clean or improve), following pattern of noun-verb pairs like 'cleanup' or 'setup'.
When people say they need a 'brushup' on French or piano, they're using the cleaning metaphor—skills get dusty if unused, so you need a quick brushup to polish them back up.
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