What are some non-CS concepts that can be defined using BNF notation?
Going with real-world things which they should be familiar with are best, even if it is completely outside of education. As you have applied the tag for adult education, I'm going to presume it is outside of normal university/college courses.

A bit of creativity and looking around can develop many an idea as long as you get outside the box. The cafeteria might be a good place to look.

entree ::= pizza | hamburger | steak
side_dish ::= corn | coleslaw | fries
beverage ::= coffee | tea | milk | soda
dessert ::= (apple|pumpkin) pie | (peach|cherry) cobbler | ice cream
meal ::= water beverage* entree side_dish+ [dessert]



  The water is mandatory (already on the table perhaps), it's possible to have as many drinks, and refills, as you wish. There is always an entree, one side dish is included, but you may have more. Finally, if you choose, you may have a desert.


If the situation is at a regular educational institution you can experiment with using degree requirement courses, and electives. There's enough there to allow the students to create their own versions as practice as well.