"Say 'cheese'" is an English-language instruction used by photographers who want their subject or subjects to smile with their lips apart and teeth showing.
In the late 19th century, different aesthetic and behavioral norms required keeping the mouth small, which led to photographers using "say prunes".[1]
Perhaps because of strong western influence, especially in the realm of photography, and perhaps because of increased numbers of western visitors after photographic equipment became widely available, "Say cheese" has also entered into the Japanese language. However, "say" is almost always dropped from the phrase, resulting in simply being "cheese." This is usually in Japanese (and written in katakana) as "chiizu" (チーズ).
Other languages have adopted this method, albeit with different words that sound similar to cheese to get the desired effect of shaping the mouth to form a smile.