Answer by Kevin Wang for What are some non-CS concepts that can be defined using BNF notation?

Mathematical expressions or natural language are good candidates for these. e.g. from http://matt.might.net/articles/grammars-bnf-ebnf/

 <expr> ::= <term> "+" <expr>
         |  <term>

 <term> ::= <factor> "*" <term>
         |  <factor>

 <factor> ::= "(" <expr> ")"
           |  <const>

 <const> ::= integer

which I think is a good candidate because it exposes the interesting recursive qualities from expansion.