“献丑” is a window into the Chinese cultural emphasis on 谦虚 (qiānxū) - modesty and humility. In traditional and many modern contexts, appearing overly confident or boastful is considered poor form and can cause others to feel uncomfortable. Using “献丑” is a social lubricant that manages expectations and maintains group harmony. A useful comparison is with Western cultural norms, particularly in the United States, where confidence is often encouraged.
By using “献丑”, the speaker deflects potential praise and frames their performance as a humble offering rather than a prideful display. This protects their own 面子 (miànzi - “face”) in case they perform poorly and gives “face” to the audience by showing deference.
“献丑” is most commonly used in social, informal, and semi-formal situations involving a performance or display of a personal skill or hobby. It is almost always said by the person who is about to perform.
It's important to note that it is not typically used in highly formal, professional contexts like a business presentation. In that case, it might be perceived as lacking confidence. A phrase like 请多指教 (qǐng duō zhǐjiào - “Please offer your guidance”) is more appropriate.