The purpose is to make the subject, assuming they speak English and are able to speak, make the "E" sound, and thus turning their mouth into shape resembling a smile.
I have a few other words I use to get clients to make this face. They are, in no particular order:
Number 6 is a popular one among little boys. Number 7 makes adults smile just because it is unexpected.
So, the desired effect is a smile, but unfortunately it can also result in what my family calls the "Chicken Run" face.
I have learned that "cheese" doesn't translate well in Spanish, but the result is humorous enough to get Hispanic clients to crack a smile. "Say queso!"
I recently did what could be called "marathon" portrait sessions at a church nativity event, where families were lined up for a free photo with a pretty backdrop.
It takes a lot of energy for me to step into the role of confident, extroverted professional photographer. It is just a facet of multi-dimensional me. :-)
Anyway, back to cheese. Where did this begin? Why cheese and not peas? What do photographers in other countries say to get their clients to pull a smile? Probably not queso.
Photo credit - PetaPixel, Rotten Tomatoes, Bright Photography