This is not a unique feature of Japanese. You can do exactly the same in Russian using a dash (which translates to a short pause in speech): "я — гамбургер" (I

This is not a unique feature of Japanese. You can do exactly the same in Russian using a dash (which translates to a short pause in speech): "я — гамбургер" (I — hamburger). In general "X — Y" means "X is Y" or another relationship between X and Y as indicated by preceding context.