Performances and Speeches: This is the most common context for a foreigner to witness a 鞠躬. Performers, artists, and public speakers will almost always bow to the audience at the end of their event to express gratitude for their attention.
Formal Apologies: When a company, celebrity, or public official makes a serious mistake, a press conference will often end with them performing a deep, sustained 鞠躬. This is a critical part of public relations, signifying deep remorse and a plea for public forgiveness.
Ceremonies and Respect for the Deceased: At funerals, memorial services, or when visiting a grave, people will 鞠躬 to show respect to the deceased. It is a solemn, non-verbal expression of grief and reverence.
Service Industry: While not as universal as in Japan, staff at high-end hotels, restaurants, or on airlines may 鞠躬 to customers to show a high level of service and respect.
What it's NOT used for: It is almost never used for everyday greetings between friends, colleagues, or with shopkeepers. Using it in a casual situation would be seen as bizarre, overly dramatic, or even sarcastic. A simple 点头 (diǎntóu), or nod, is the appropriate gesture.